Hjem
Andreas Leopold Knutsens bilde

Andreas Leopold Knutsen

Professor
  • E-postAndreas.Knutsen@uib.no
  • Telefon+47 55 58 49 31
  • Besøksadresse
    Realfagbygget, Allégt. 41
  • Postadresse
    Postboks 7803
    5020 Bergen
  1. On kth-order embeddings of $K3$ surfaces and Enriques surfaces, Manuscripta Mathematica 104, 211-237 (2001).
  2. Smooth curves on projective K3 surfaces, Mathematica Scandinavica 90, 215-231 (2002).
  3. Gonality and Clifford index of curves on K3 surfaces, Archiv der Mathematik 80, 235-238 (2003).
  4. Higher order birational embeddings of Del Pezzo surfaces, Mathematische Nachrichten 254-255, 183-196 (2003).
  5. Exceptional curves on Del Pezzo surfaces, Mathematische Nachrichten 256, 58-81 (2003).
  6. Rational curves in Calabi-Yau threefolds, with T. Johnsen, Communications in Algebra 31, 3917-3953 (2003). Errata and Addenda: ``Rational curves in Calabi-Yau threefolds'', Communications in Algebra 33, 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, 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. 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, 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. 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 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). Corrigendum.
  31. On the existence of curves with Ak-singularities on K3 surfaces, with C. Galati, Mathematical Research Letters 21, 1069--1109 (2014).
  32. Projective normality and the generation of the ideal of an Enriques surface, with A. F. Lopez, Advances in Geometry 15, 339--348 (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. 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).
  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 (2016), doi:10.1007/s12215-016-0284-4 (Online first)
  36. A note on deformations of regular embeddings, with C. Ciliberto, F. Flamini and C. Galati, Rendiconti del Circolo Matematico di Palermo, II. Ser (2017) 66, 53--63. Errata Corrige.
  37. Moduli of nodal curves on K3 surfaces, with C. Ciliberto, F. Flamini and C. Galati, Advances in Mathematics, 309, 624--654 (2017).
  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 DOI 10.1515/crelle-2016-0029 (Ahead of Print).
  39. Degeneration of differentials and moduli of nodal curves on K3 surfaces, with C. Ciliberto, F. Flamini and C. Galati, arXiv:1701.07224, to appear in the Proceedings of the Conference ``Local and Global Methods in Algebraic Geometry'', in honor of Lawrence Ein, Contemp. Math. Series AMS, 2017.
  40. Wall divisors and algebraically coisotropic subvarieties of irreducible holomorphic symplectic manifolds, with M. Lelli-Chiesa and G. Mongardi, arXiv:1507.06891, to appear in Transactions of the American Mathematical Society.
Vitenskapelig artikkel
  • 2020. On the locus of Prym curves where the Prym-canonical map is not an embedding. Arkiv för matematik. 71-85 .
  • 2020. Moduli of curves on Enriques surfaces. Advances in Mathematics.
  • 2020. Global sections of twisted normal bundles of K3 surfaces and their hyperplane sections . Rendiconti Lincei - Matematica e Applicazioni. 57-79.
  • 2020. A note on Severi varieties of nodal curves on Enriques surfaces. Springer INdAM Series. 29-36.
  • 2019. Wall divisors and algebraically coisotropic subvarieties of irreducible holomorphic symplectic manifolds. Transactions of the American Mathematical Society. 1403-1438.
  • 2019. Severi Varieties and Brill-Noether theory of curves on abelian surfaces. Journal für die Reine und Angewandte Mathematik. 161-200.
  • 2019. Half Nikulin surfaces and moduli of Prym curves. Journal of the Institute of Mathematics of Jussieu. 1-38.
  • 2018. Degeneration of differentials and moduli of nodal curves on K3 surfaces. Contemporary Mathematics. 59-79.
  • 2017. Moduli of nodal curves on K3 surfaces. Advances in Mathematics. 624-654.
  • 2017. A note on deformations of regular embeddings. Rendiconti del circolo matematico di Palermo. 53-63.
  • 2017. A few questions about curves on surfaces. Rendiconti del circolo matematico di Palermo. 195-204.
  • 2015. Projective normality and the generation of the ideal of an Enriques surface. Advances in Geometry. 339-348.
  • 2015. Brill–Noether theory of curves on Enriques surfaces II: the Clifford index. Manuscripta mathematica. 193-237.
  • 2015. Appendix to "Generalized Lazarsfeld-Mukai bundles and a conjecture of Donagi and Morrison" by M. Lelli-Chiesa. Advances in Mathematics.
  • 2014. On the existence of curves with Ak-singularities on K3 surfaces. Mathematical Research Letters. 1069-1109.
  • 2014. On k-gonal loci in Severi varieties on general K3 surfaces and rational curves on hyperkähler manifolds. Journal des Mathématiques Pures et Appliquées. 473-494.
  • 2013. Smooth, isolated curves in families of Calabi-Yau threefolds in homogeneous spaces. Journal of the Korean Mathematical Society. 1033-1050.
  • 2013. Seshadri constants of K3 surfaces of degrees 6 and 8. International mathematics research notices. 4072-4084.
  • 2013. Negative curves on algebraic surfaces. Duke mathematical journal. 1877-1894.
  • 2012. On the proof of the genus bound for Enriques-Fano threefolds. Journal of the Ramanujan Mathematical Society. 375-395.
  • 2012. On the birationality of the adjunction mapping of projective varieties. Journal of the Ramanujan Mathematical Society. 51-58.
  • 2012. On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds. Transactions of the American Mathematical Society. 5243-5264.
  • 2012. Geometry of rays-positive manifolds. Collectanea Mathematica. 375-391.
  • 2011. On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds. Journal of differential geometry. 483-518.
  • 2009. On two conjectures for curves on K3 surfaces. International Journal of Mathematics. 1547-1560.
  • 2009. On secant spaces to Enriques surfaces. Bulletin of the Belgian Mathematical Society Simon Stevin. 907-931.
  • 2009. On families of rational curves in the Hilbert square of a surface (with an appendix by E. Sernesi). The Michigan mathematical journal. 639 -682.
  • 2009. Moving curves and seshadri constants. Mathematical Research Letters. 711-719.
  • 2009. Brill-Noether theory of curves on Enriques surfaces I: the positive cone and gonality. Mathematische Zeitschrift. 659-690.
  • 2009. A primer on Seshadri constants. Contemporary Mathematics. 33-70.
  • 2008. Remarks on families of singular curves with hyperellipticnormalizations. Indagationes mathematicae. 217-238.
  • 2008. Nodal Curves with General Moduli on K3 Surfaces. Communications in Algebra. 3955-3971.
  • 2008. A Note on Seshadri constants on general K3 surfaces. Comptes rendus. Mathematique. 1079-1081.
  • 2007. Singular curves on a K3 surface and linear series on their normalizations. International Journal of Mathematics. 671-693.
  • 2007. On the surjectivity of Gaussian maps for curves on Enriques surfaces. Advances in Geometry. 215-247.
  • 2007. A sharp vanishing theorem for line bundles on K3 or Enriques surfaces. Proceedings of the American Mathematical Society. 3495-3498.
  • 2006. On varieties that are uniruled by lines. Compositio Mathematica. 889-906.
  • 2003. Rational curves in Calabi-Yau threefolds. Communications in Algebra. 3917-3953.
  • 2003. Higher order birational embeddings of Del Pezzo surfaces. Mathematische Nachrichten. 183-196.
  • 2003. Gonality and Clifford index of curves on $K3$ surfaces. Archiv der Mathematik. 235-238.
  • 2003. Exceptional curves on Del Pezzo surfaces. Mathematische Nachrichten. 58-81.
  • 2002. Smooth curves on projective K3 surfaces. Mathematica Scandinavica. 215-231.
  • 2001. On $k$th-order embeddings of $K3$ surfaces and Enriques surfaces. Manuscripta mathematica. 211-237.
Vitenskapelig monografi
  • 2004. $K3$ projective models in scrolls.
Fagbok
  • 2011. Combinatorial aspects of commutative algebra and algebraic geometry. Proceedings of the Abel Symposium held in Voss, June 1–4, 2009. Springer.
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
  • 2012. Recent developments and open problems in linear series. 48 sider.
Errata
  • 2017. Erratum to: A note on deformations of regular embeddings (Rend. Circ. Mat. Palermo, II. Ser, 10.1007/s12215-016-0276-4). Rendiconti del circolo matematico di Palermo. 65-67.
  • 2017. Corrigendum to "On k-gonal loci in Severi varieties on general K3 surfaces and rational curves on hyperkahler manifolds" [J. Math. Pures Appl. 101 (4) (2014) 473-494] (S0021782413000962)(10.1016/j.matpur.2013.06.010). Journal des Mathématiques Pures et Appliquées. 665-666.

Se fullstendig oversikt over publikasjoner i CRIStin.

Kurverflater og i trefoldigheter,  moduli og deformasjoner av kurver, Brill-Noether teori og syzygier av  algebraiske kurver, positivitet av linjebunter på algebraiske varieteter, birasjonal geometri og Minimal-Modell-Programmet (Mori-teori).