Andreas Leopold Knutsen

Professor in Mathematics at the University of Bergen (Norway)

Academic Employment History and Qualifications
Research field
Research Interests
"My" K3 surfaces
Publications
Recent activities (conferences etc.)
Students
Teaching
my face
Office
4a3f
E-mail address:
andreas.knutsen at math.uib.no
Phone:
(47) 5558 49 31
Facsimile:
(47) 5558 9672
Personal information
Born May 12th, 1975, in Haugesund, Norway
Italian and Norwegian citizen

Snail mail address
Department of Mathematics
University of Bergen
Postboks 7800
N-5020 BERGEN


Academic Employment History and Qualifications

  • September 2013-- Full Professor in Mathematics at the Department of Mathematics, University of Bergen, Norway
  • 2013 Awarded National Scientific Qualification (Abilitazione Scientifica Nazionale) 2012 as Full Professor (Professore ordinario di prima fascia) in the competition sector 01/A2 GEOMETRIA E ALGEBRA in Italy. Renewed 2019
  • November 2007-September 2013 Associate Professor in Mathematics at the Department of Mathematics, University of Bergen, Norway
  • November 2005-October 2007 Marie Curie Fellow at the Department of Mathematics, University of Roma Tre, Italy
  • August 2003 -- July 2005 Post-doctor at the Department of Mathematics, University of Oslo, Norway
  • July 2001 -- June 2003 Post-doctor at the Department of Mathematics, University of Essen, Germany (grant from the Research Council of Norway)

  • Research field

    Algebraic Geometry

    Algebraic Geometry at UiB


    Research Interests

    Curves on surfaces and in threefolds, moduli and deformations of projective varieties, in particular (singular) curves and surfaces, Brill-Noether theory and syzygies of (singular) algebraic curves, positivity questions on line bundles on algebraic varieties, birational geometry and Minimal Model Program (Mori theory).

    "My" K3 surfaces

    Here they are (how much did I pay the authors? )

    Publications

      Peer-reviewed Research Monographs

    1. K3 projective models in scrolls, with T. Johnsen, Springer Lecture Notes in Mathematics 1842, 164 pages (2004).
    2. Peer-reviewed Research Articles

    3. On kth-order embeddings of $K3$ surfaces and Enriques surfaces, Manuscripta Mathematica 104, 211-237 (2001).
    4. Smooth curves on projective K3 surfaces, Mathematica Scandinavica 90, 215-231 (2002).
    5. Gonality and Clifford index of curves on K3 surfaces, Archiv der Mathematik 80, 235-238 (2003).
    6. Higher order birational embeddings of Del Pezzo surfaces, Mathematische Nachrichten 254-255, 183-196 (2003).
    7. Exceptional curves on Del Pezzo surfaces, Mathematische Nachrichten 256, 58-81 (2003).
    8. Rational curves in Calabi-Yau threefolds, with T. Johnsen, Communications in Algebra 31, 3917-3953 (2003) (with an "Errata and Addenda").
    9. On varieties that are uniruled by lines, with C. Novelli and A. Sarti, Compositio Mathematica 142, 889-906 (2006).
    10. Surjectivity of Gaussian maps for curves on Enriques surfaces, with A. F. Lopez, Advances in Geometry 7, 215-247 (2007).
    11. Singular curves on a K3 surface and linear series on their normalizations, with F. Flamini and G. Pacienza, International Journal of Mathematics 18, 671-693 (2007).
    12. A sharp vanishing theorem for line bundles on K3 or Enriques surfaces, with A. F. Lopez, Proceedings of the American Mathematical Society 135, 3495-3498 (2007).
    13. A note on Seshadri constants on general K3 surfaces, Comptes rendus de l'Académie des sciences Paris, Ser.I, 346, 1079-1081 (2008).
    14. Nodal curves with general moduli on K3 surfaces, with F. Flamini, G. Pacienza and E. Sernesi, Communications in Algebra 36, 3955-3971 (2008).
    15. Remarks on families of curves with hyperelliptic normalizations, Indagationes Mathematicae 19, 217-238 (2008).
    16. Brill-Noether theory for curves on Enriques surfaces, I: the positive cone and gonality, with A. F. Lopez, Mathematische Zeitschrift 261, 659-690 (2009).
    17. Moving curves and Seshadri constants, with W.Syzdek and T. Szemberg, Mathematical Research Letters 16, 711-719 (2009).
    18. On secant spaces to Enriques surfaces, Bulletin of the Belgian Mathematical Society Simon Stevin 16, 907-931 (2009).
    19. On families of rational curves in the Hilbert square of a surface (with an appendix by E. Sernesi), with F. Flamini and G. Pacienza, Michigan Mathematical Journal 58, 639-682 (2009).
    20. On two conjectures for curves on K3 surfaces, International Journal of Mathematics, 20, 1547-1560 (2009).
    21. On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds, with A. F. Lopez and R. Munoz, Journal of Differential Geometry 88, 483-518 (2011).
    22. Recent developments and open problems in linear series, with Th. Bauer, C. Bocci, S. Cooper, S. Di Rocco, M. Dumnicki, B. Harbourne, K. Jabbusch, A. Küronya, R. Miranda, J. Roé, H. Schenck, T. Szemberg and Z. Teitler, in ``Contributions to Algebraic Geometry'', EMS Series of Congress Reports, Impanga Lecture Notes (Piotr Pragacz, ed.),European Mathematical Society Publishing House, 93-140 (2012).
    23. On the birationality of the adjunction mapping of projective varieties, Journal of the Ramanujan Mathematical Society 27, 51-58 (2012).
    24. On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds, Transactions of the American Mathematical Society 364, 5243-5264 (2012).
    25. Geometry of rays-positive manifolds, with M. C. Beltrametti, A. Lanteri and C. Novelli, Collectanea Mathematica 63, 375-391 (2012).
    26. On the proof of the genus bound for Enriques-Fano threefolds, with A. F. Lopez and R. Munoz, Journal of the Ramanujan Mathematical Society 27, 375-395 (2012).
    27. Seshadri constants of K3 surfaces of degrees 6 and 8, with C. Galati, International Mathematics Research Notices IMRN 2013, issue 17, 4072-4084 (2013).
    28. Negative curves on algebraic surfaces, with Th. Bauer, B. Harbourne, A. Küronya, S. Müller-Stach, X. Roulleau, T. Szemberg, Duke Mathematical Journal 162, 1877-1894 (2013).
    29. Smooth, isolated curves in families of Calabi-Yau threefolds in homogeneous spaces, Journal of the Korean Mathematical Society 50, 1033-1050 (2013).
    30. On k-gonal loci in Severi varieties on general K3 surfaces and rational curves on hyperkähler manifolds, with C. Ciliberto, Journal de Mathématiques Pures et Appliquées 101, 473-494 (2014) (with a "Corrigendum").
    31. On the existence of curves with Ak-singularities on K3 surfaces, with C. Galati, Mathematical Research Letters 21, 1069-1109 (2014).
    32. Appendix, with M. Lelli-Chiesa, to Generalized Lazarsfeld-Mukai bundles and a conjecture of Donagi and Morrison, by M. Lelli-Chiesa, Advances in Mathematics 268, 529-563 (2015).
    33. Brill-Noether theory of curves on Enriques surfaces, II. The Clifford index, with A. F. Lopez, Manuscripta Mathematica 147, 193-237 (2015).
    34. Projective normality and the generation of the ideal of an Enriques surface, with A. F. Lopez, Advances in Geometry 15, 339-348 (2015).
    35. A few questions about curves on surfaces, with C. Ciliberto, J. Lesieutre, V. Lozovanu, R. Miranda, Y. Mustopa and D. Testa, Rendiconti del Circolo Matematico di Palermo, II. Ser 66, 195-204 (2017)
    36. A note on deformations of regular embeddings, with C. Ciliberto, F. Flamini and C. Galati, Rendiconti del Circolo Matematico di Palermo, II. Ser 66, 53-63 (2017) (with an "Erratum").
    37. Moduli of nodal curves on K3 surfaces, with C. Ciliberto, F. Flamini and C. Galati, Advances in Mathematics, 309, 624-654 (2017).
    38. Degeneration of differentials and moduli of nodal curves on K3 surfaces, with C. Ciliberto, F. Flamini and C. Galati, in ``Local and Global Methods in Algebraic Geometry'', Contemporary Mathematics 712, 59-79, Amer. Math. Soc., Providence, RI, 2018.
    39. Severi Varieties and Brill-Noether theory of curves on abelian surfaces, with M. Lelli-Chiesa and G. Mongardi, Journal für die Reine und Angewandte Mathematik, 749, 161-200 (2019).
    40. Wall divisors and algebraically coisotropic subvarieties of irreducible holomorphic symplectic manifolds, with M. Lelli-Chiesa and G. Mongardi, Transactions of the American Mathematical Society 371, 1403-1438 (2019).
    41. A note on Severi varieties of nodal curves on Enriques surfaces, with Ciro Ciliberto, Thomas Dedieu and Concettina Galati, in "Birational Geometry and Moduli Spaces", Springer INdAM Series 39,29-36 (2018).
    42. Half Nikulin surfaces and moduli of Prym curves, with Margherita Lelli-Chiesa and Alessandro Verra, Journal of the Institute of Mathematics of Jussieu (2019), 1-38, doi:10.1017/S1474748019000574.
    43. Global sections of twisted normal bundles of K3 surfaces and their hyperplane sections , Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31, 57-79 (2020).
    44. On the locus of Prym curves where the Prym-canonical map is not an embedding, with Ciro Ciliberto, Thomas Dedieu and Concettina Galati, Arkiv för Matematik 58, 71--85 (2020).
    45. Moduli of curves on Enriques surfaces, with Ciro Ciliberto, Thomas Dedieu and Concettina Galati, Advances in Mathematics 365 (2020), 107010.
    46. Brill-Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree, with Michael Hoff, Geometriae Dedicata, doi.org/10.1007/s10711-020-00565-z (2020), with Ancillary Macaulay2 file.
    47. Moduli of non-standard Nikulin surfaces in low genus, with Margherita Lelli-Chiesa and Alessandro Verra, arXiv:1802.01201, to appear in Annali della Scuola Normale Superiore di Pisa - Classe di Scienze.
    48. On moduli spaces of polarized Enriques surfaces, Journal de Mathématiques Pures et Appliquées (2020), doi.org/10.1016/j.matpur.2020.10.003.
    49. Genus two curves on abelian surfaces, with Margherita Lelli-Chiesa, arXiv:1901.07603, to appear in Annales scientifiques de l'École Normale Supérieure.
    50. Peer-reviewed Expository Articles

    51. A primer on Seshadri constants, with Th. Bauer, S. Di Rocco, B. Harbourne, M. Kapustka, W. Syzdek and T. Szemberg, Contemporary Mathematics 496, "Interactions of Classical and Numerical Algebraic Geometry", in honor of Andrew J. Sommese, 33-70 (2009).
    52. Submitted Research Articles available on ArXiv

    53. Irreducible unirational and uniruled components of moduli spaces of polarized Enriques surfaces, with Ciro Ciliberto, Thomas Dedieu and Concettina Galati, arXiv:1809.10569.

    Recent activities (conferences etc.)

  • Speaker in the conference Classical Algebraic Geometry and related topics, in honor of Mauro C. Beltrametti on the occasion of his 70th birthday, University of Genova Department of Mathematics July 2--6, 2018.
  • Speaker in the G.T.M. Seminar Genova, Torino, Milano Seminar: Some Topics in Commutative Algebra and Algebraic Geometry, Politecnico di Torino, November 30--December 1, 2017.
  • Speaker in the conference Workshop "Modern Algebra and Classical Geometry", on the occasion of Edoardo Sernesi's 70th birthday, June 21-24, 2017, Trento.
  • Speaker in the workshop "Local negativity and positivity", Hannover, March 7-10, 2017
  • Speaker in the workshop Journées de Géométrie Algébrique Poitiers - Bordeaux, Poitiers, November 24-25, 2016
  • Speaker in the workshop Birational geometry of surfaces at the University of Roma Tor Vergata, January 11-15, 2016
  • Organiser of the Mini-Workshop Singular Curves on K3 Surfaces and Hyperkähler Manifolds at the Mathematisches Forschungsinstitut Oberwolfach, November 8-14, 2015.
  • Sabbatical in Rome, at the Universities Roma Sapienza , Roma Tor Vergata and Roma Tre, May 2014-August 2015.
  • Participant in the Oberwolfach Mini-workshop Negative Curves on Algebraic Surfaces, Mathematisches Forschungsinstitut Oberwolfach, February 23 - March 1, 2014.
  • Lecturer of mini-course "Linear series on singular curves on K3 surfaces: Vector bundle methods and degenerations" at the Hausdorff Research Institute for Mathematics in Bonn, January 27 - 31, 2014.
  • Organiser of Workshop on Severi Varieties and Hyperkähler Manifolds, University Rome Tor Vergata, Italy, November 4-8, 2013.
  • Visiting Professor at the Department of Mathematics of the University of Poitiers, France, March 12-April 14, 2012.
  • Participant in the program Algebraic Geometry with a view towards applications, Institut Mittag-Leffler, Stockholm, Sweden, April 15-June 15, 2011.
  • Participant in the Oberwolfach Mini-workshop Linear Series on Algebraic Varieties, Mathematisches Forschungsinstitut Oberwolfach, Germany, October 3-9, 2010.
  • Visiting Professor (funded by INDAM) at the Department of mathematics of the University of Genoa, Italy, June 18-August 18, 2010, and July 3-August 6, 2009.
  • Organiser of The Abel Symposium 2009, Voss, Norway, June 1-4, 2009.

  • Students

  • Nils Henry Williams Rasmussen, PhD, Bergen, October 2010, title of thesis: Two aspects of Brill-Noether theory: the Green conjecture for curves on K3 surfaces, and applications to scroll codes.
  • Simone Billi, Laurea magistrale, Università di Bologna, September 2020, title of thesis: Reider's theorem on complex surfaces and a generalization.
  • Roberto Laface, Laurea magistrale, Università di Milano, July 2013, title of thesis: On Zariski decompositions and the orbibundle Miyaoka-Yau-Sakai-inequality.
  • Davide Cesare Veniani, Laurea Magistrale, Università di Pavia, November 2012, title of thesis: On the Clifford invariants of an algebraic curve.
  • Gard Sæbø, Master, Bergen, June 2012, title of thesis: Gonality of points in Brill-Noether loci of the moduli space of curves.
  • Sturla Bingen, Master, Bergen, December 2009 (joint supervision with K. Ranestad, University of Oslo), title of thesis: Dualgraden til noen determinentelle varieteter (The dual degree of some determinantal varieties).
  • Jonas Eidesen, René Langøen, Karl Fredrik Munthe, joint bachelor's thesis, University of Bergen, December 2019 (joint supervision with M. Førre, Dept. of Physics), title of thesis: Diraclikningen for hydrogenlignende atomer: En komplett løsning (Dirac's equation for hydrogen-like atoms: A complete solution).
  • Kim Haugland, Bachelor, Bergen 2014, title of thesis: Abel's Theorem on compact Riemann surfaces.
  • Franco Rota, Università di Pavia, bachelor's thesis June 2013 (Bergen), title of thesis: The Riemann-Roch Theorem for algebraic curves.
  • Espen Eidsvåg, Bachelor, Bergen, June 2010, title of thesis: Ikke-Euklidsk geometri (Non-Euclidean geometry).
  • Ørjan Storheim, Bachelor, Bergen, June 2010, title of thesis: Euklidsk og ikkje-Euklidsk geometri med omsyn på hyperbolsk geometri (Euclidean and non-Euclidean geometry with focus on hyperbolic geometry).
  • Gard Sæbø, Bachelor, Bergen, June 2010, title of thesis: An introduction to sheaf cohomology.
  • Karen Johanne Sætrevik, Bachelor, Bergen, June 2009, title of thesis: Eit aksiomatisk innblikk i euklidsk geometri (An axiomatic overview of Euclidean geometry).

  • Teaching

    Course Semester
    MAT100 Introductory course in Mathematics   fall 2020
    MAT232 Funksjonalanalyse   spring 2020
    MAT211 Reell analyse   fall 2019
    MAT322 Algebraisk Geometri II   spring 2019
    MAT111 Grunnkurs i matematikk I ("Calculus I")   autumn 2018
    MAT111 Grunnkurs i matematikk I ("Calculus I")   autumn 2017
    MAT292 Prosjektarbeid i matematikk   spring 2017
    MAT111 Grunnkurs i matematikk I ("Calculus I")   autumn 2016
    MAT229 Algebraisk geometri I + MAT320 Introduction to Sheaves and Schemes   spring 2009
    MAT211 Reell analyse   fall 2015
    PhD course "Curve e sistemi lineari su superfici K3", at the University Roma Tor Vergata (Italy)   Jan.-Feb. 2015
    Mini-course "Linear series on singular curves on K3 surfaces: Vector bundle methods and degenerations", at the Hausdorff Research Institute for Mathematics (Bonn, Germany)   Jan. 27-31, 2014
    MAT243 Mangfoldigheter (Manifolds)   spring 2014
    MAT214 Kompleks analyse   fall 2013
    MAT243 Mangfoldigheter (Manifolds)   spring 2013
    MAT322 Algebraisk geometri II   fall 2012
    PhD course "Systèmes linéaires et courbes rationnelles sur surfaces K3", at the University of Poitiers (France)   March/April 2012
    MAT112 Grunnkurs i matematikk II ("Calculus II")   spring2012
    MAT242 Topologi   autumn 2011
    MAT112 Grunnkurs i matematikk II ("Calculus II")   spring2011
    MAT242 Topologi   autumn 2010
    MNF130 Diskrete strukturer   spring 2010
    MAT111 Grunnkurs i matematikk I ("Calculus I")   autumn 2009
    MAT321/322 Algebraisk geometri I, II   spring 2009
    MAT111 Grunnkurs i matematikk I ("Calculus I")   autumn 2008
    MAT220 Algebra   spring 2008




    Andreas Leopold Knutsen
    Last modified: 03/11/2020