Andreas Leopold Knutsen

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

Research field
Research Interests
Publications
Students
Teaching
my face
Office
531 (Carl L. Godskes hus)
E-mail address:
andreas.knutsen at math.uib.no
Phone:
(47) 5558 49 31
Facsimile:
(47) 5558 9672
Snail mail address:
Department of Mathematics
University of Bergen
Postboks 7800
N-5020 BERGEN
Personal information
Born May 12th, 1975, in Haugesund, Norway
Italian and Norwegian citizen


Research field

Algebraic Geometry

Research Interests

Curves on surfaces and in threefolds, moduli and deformations of (singular) curves, 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).

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 Ak-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).

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.
  • Davide Cesare Veniani, Laurea Magistrale, Università di Pavia, November 2012 (joint supevision with Gian Pietro Pirola), title of thesis: On the Cliffords 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).
  • 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
    MAT243 Mangfoldigheter (Manifolds)   spring 2013
    MAT322 Algebraisk geometri II   fall 2012
    PhD course "Systèmes linéaires et courbes rationnelles sur surfaces K3" (Université Poitiers, France)   march/april2012
    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: April 29th, 2013