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

Academic Employment History and Qualifications

Research field

Algebraic Geometry at UiB

Research Interests

"My" K3 surfaces

Publications

Peer-reviewed Research Monographs

1. K3 projective models in scrolls, with T. Johnsen, Springer Lecture Notes in Mathematics 1842, 164 pages (2004).

Peer-reviewed Research Articles

2. On kth-order embeddings of $K3$ surfaces and Enriques surfaces, Manuscripta Mathematica 104, 211-237 (2001).
3. Smooth curves on projective K3 surfaces, Mathematica Scandinavica 90, 215-231 (2002).
4. Gonality and Clifford index of curves on K3 surfaces, Archiv der Mathematik 80, 235-238 (2003).
5. Higher order birational embeddings of Del Pezzo surfaces, Mathematische Nachrichten 254-255, 183-196 (2003).
6. Exceptional curves on Del Pezzo surfaces, Mathematische Nachrichten 256, 58-81 (2003).
7. Rational curves in Calabi-Yau threefolds, with T. Johnsen, Communications in Algebra 31, 3917-3953 (2003) (with an "Errata and Addenda").
8. On varieties that are uniruled by lines, with C. Novelli and A. Sarti, Compositio Mathematica 142, 889-906 (2006).
9. Surjectivity of Gaussian maps for curves on Enriques surfaces, with A. F. Lopez, Advances in Geometry 7, 215-247 (2007).
10. 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).
11. 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).
12. A note on Seshadri constants on general K3 surfaces, Comptes rendus de l'Académie des sciences Paris, Ser.I, 346, 1079-1081 (2008).
13. Nodal curves with general moduli on K3 surfaces, with F. Flamini, G. Pacienza and E. Sernesi, Communications in Algebra 36, 3955-3971 (2008).
14. Remarks on families of curves with hyperelliptic normalizations, Indagationes Mathematicae 19, 217-238 (2008).
15. Brill-Noether theory for curves on Enriques surfaces, I: the positive cone and gonality, with A. F. Lopez, Mathematische Zeitschrift 261, 659-690 (2009).
16. Moving curves and Seshadri constants, with W.Syzdek and T. Szemberg, Mathematical Research Letters 16, 711-719 (2009).
17. On secant spaces to Enriques surfaces, Bulletin of the Belgian Mathematical Society Simon Stevin 16, 907-931 (2009).
18. 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).
19. On two conjectures for curves on K3 surfaces, International Journal of Mathematics, 20, 1547-1560 (2009).
20. 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).
21. 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).
22. On the birationality of the adjunction mapping of projective varieties, Journal of the Ramanujan Mathematical Society 27, 51-58 (2012).
23. On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds, Transactions of the American Mathematical Society 364, 5243-5264 (2012).
24. Geometry of rays-positive manifolds, with M. C. Beltrametti, A. Lanteri and C. Novelli, Collectanea Mathematica 63, 375-391 (2012).
25. 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).
26. Seshadri constants of K3 surfaces of degrees 6 and 8, with C. Galati, International Mathematics Research Notices IMRN 2013, issue 17, 4072-4084 (2013).
27. 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).
28. Smooth, isolated curves in families of Calabi-Yau threefolds in homogeneous spaces, Journal of the Korean Mathematical Society 50, 1033-1050 (2013).
29. 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").
30. On the existence of curves with A_k-singularities on K3 surfaces, with C. Galati, Mathematical Research Letters 21, 1069-1109 (2014).
31. 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).
32. Brill-Noether theory of curves on Enriques surfaces, II. The Clifford index, with A. F. Lopez, Manuscripta Mathematica 147, 193-237 (2015).
33. Projective normality and the generation of the ideal of an Enriques surface, with A. F. Lopez, Advances in Geometry 15, 339-348 (2015).
34. 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)
35. 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").
36. Moduli of nodal curves on K3 surfaces, with C. Ciliberto, F. Flamini and C. Galati, Advances in Mathematics, 309, 624-654 (2017).
37. 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.
38. 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).
39. 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).
40. 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).
41. 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.
42. 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).
43. 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).
44. Moduli of curves on Enriques surfaces, with Ciro Ciliberto, Thomas Dedieu and Concettina Galati, Advances in Mathematics 365 (2020), 107010.
45. 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.
46. 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.
47. On moduli spaces of polarized Enriques surfaces, Journal de Mathématiques Pures et Appliquées (2020), doi.org/10.1016/j.matpur.2020.10.003.
48. Genus two curves on abelian surfaces, with Margherita Lelli-Chiesa, arXiv:1901.07603, to appear in Annales scientifiques de l'École Normale Supérieure.

Peer-reviewed Expository Articles

49. 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).

Submitted Research Articles available on ArXiv

50. 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.)

Students

Teaching