Andreas Leopold Knutsen

Associate Professor in Pure Mathematics at the University of Bergen (Norway)

Research field

Research Interests

Publications (in refereed journals)

1. On kth-order embeddings of $K3$ surfaces and Enriques surfaces, Manuscripta Mathematica 104, 2, 211-237 (2001).
2. Smooth curves on projective K3 surfaces, Mathematica Scandinavica 90, 2, 215-231 (2002).
3. Gonality and Clifford index of curves on K3 surfaces, Archiv der Mathematik 80, 3, 235-238 (2003).
4. Higher order birational embeddings of Del Pezzo surfaces, Mathematische Nachrichten 254-255, 1, 183-196 (2003).
5. Exceptional curves on Del Pezzo surfaces, Mathematische Nachrichten 256, 1, 58-81 (2003).
6. Rational curves in Calabi-Yau threefolds, with T. Johnsen, Communications in Algebra 31, 8, 3917-3953 (2003). Errata and Addenda: ``Rational curves in Calabi-Yau threefolds'', Communications in Algebra 33, 6, 2075--2076 (2005).
7. K3 projective models in scrolls, with T. Johnsen, Springer Lecture Notes in Mathematics 1842, 164 pages (2004).
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, No. 6, 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, No. 11, 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 (2), 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, No.3, 659-690 (2009).
16. Moving curves and Seshadri constants, with W.Syzdek and T. Szemberg, Mathematical Research Letters 16, No. 4, 711-719 (2009).
17. 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).
18. On secant spaces to Enriques surfaces, Bulletin of the Belgian Mathematical Society Simon Stevin 16, No. 5, 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 (3), 639-682 (2009).
20. On two conjectures for curves on K3 surfaces, International Journal of Mathematics, 20 (12), 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. 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. 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).
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, rns174, 13 pages, doi:10.1093/imrn/rns174 (2012).
28. Negative curves on algebraic surfaces , with Th. Bauer, B. Harbourne, A. Küronya, S. Müller-Stach, X. Roulleau, T. Szemberg, to appear in Duke Mathematical Journal; arXiv:1109.1881 (2012).
29. On k-gonal loci in Severi varieties on general K3 surfaces and rational curves on hyperkähler manifolds, with C. Ciliberto, to appear in Journal de Mathématiques Pures et Appliquées; arXiv:1204.4838 (2013).
30. On the existence of curves with A_k-singularities on K3 surfaces, with C. Galati, arXiv:1107.4568 (2012).
31. Smooth, isolated curves in families of Calabi-Yau threefolds in homogeneous spaces, arXiv:math/0110220 (2012).

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