Leiter Lehrstuhl Algebraische Geometrie
Aktuelles/Upcoming events
Editorial work/Herausgebertätigkeit
Research/Forschungsgebiet
My field of work is algebraic geometry. A significant part of my research is concerned with the study of the geometry and topology of various moduli spaces. Among other things I am interested in moduli of curves, enumerative geometry, vector bundles on curves, abelian varieties and theta functions, Prym varieties, K3 surfaces, Brill-Noether type problems and syzygies of algebraic varieties.Current Projects/Laufende Projekte
Publications/Veröffentlichungen
The geometry of the moduli space of curves of genus 23 dvi pdf
Brill-Noether loci and the gonality stratification of M_g
dvi pdf
J. reine angewandte Mathematik 539 (2001), 185-200
Divisors on M_{g,g+1} and the minimal resolution conjecture for points on canonical curves
dvi pdf
(with M. Mustata and M. Popa), Annales Scientifiques de L'Ecole Normale Superieure 36 (2003), 553-581
The Mori cones of moduli spaces of pointed curves of small genus
dvi pdf
(with A. Gibney),
Transactions of the American Mathematical Society 355 (2003), 1183-1199
Regular components of moduli spaces of stable maps
dvi pdf
Proceedings of the American Mathematical Society 131 (2003), 2027-2036
Gaussian maps, Gieseker-Petri loci and large theta-characteristics
dvi pdf
J. reine angewandte Mathematik 581 (2005), 151-174
Effective divisors on M_g, curves on K3 surfaces and the Slope Conjecture dvi pdf
(with M. Popa)
Journal of Algebraic Geometry 14 (2005), 241-267
Syzygies of curves and the effective cone of M_g dvi pdf
Duke Mathematical Journal 135(2006), 53-98
Higher ramification and varieties of secant divisors on the generic curve
dvi pdf
Journal of the London Mathematical Society 78 (2008), 418-440
The global geometry of the moduli space of curves dvi pdf
Algebraic Geometry Seattle 2005, Proceedings of Symposia in Pure Mathematics 80 (2009), 125-147
Koszul divisors on moduli spaces of curves dvi pdf
American Journal of Mathematics 131 (2009), 819-867
The birational type of the moduli space of even spin curves dvi pdf
Advances in Mathematics 223 (2010), 433-443
Rational maps between moduli spaces of curves and Gieseker-Petri divisors dvi pdf
Journal of Algebraic Geometry 19 (2010), 243-284
The Kodaira dimension of the moduli space of Prym varieties dvi pdf
(with K. Ludwig) Journal of the European Mathematical Society 12 (2010), 755-795
The Fermat cubic and special Hurwitz loci in M_g
dvi pdf
Bulletin of the Belgian Mathematical Society "Simon Stevin" 5 (2009), 831-851.
Special volume dedicated to the conference "Linear series and subschemes"-Ghent 2007
Aspects of the birational geometry of M_g dvi
pdf
"Geometry of Riemann surfaces and their moduli spaces"
Surveys in Differential Geometry Vol. 14 (2010), 57-111
Brill-Noether geometry on moduli spaces of spin curves
dvi pdf
Classification of algebraic varieties-Schiermonnikoog 2009, 259-276
C. Faber, G. van der Geer, E. Looijenga editors, EMS Congress Reports 2011
Koszul cohomology and applications to moduli dvi pdf
(with M. Aprodu) Grassmannians, moduli spaces and vector bundles
Clay Mathematics Proceedings, E. Previato editor, Volume 14, 2011, 25-50
The Green Conjecture for smooth curves lying on arbitrary K3 surfaces
dvi pdf
(with M. Aprodu) Compositio Mathematica 147 (2011), 839-851
The maximal rank conjecture and rank two Brill-Noether theory
dvi pdf
(with A. Ortega)
Pure and Applied Mathematics Quarterly 7 (2011), 1265-1296
Special volume dedicated to the memory of E. Viehweg.
Higher rank Brill-Noether theory on sections of K3 surfaces
dvi pdf
(with A. Ortega) International Journal of Mathematics 23 (2012) 1250075
Moduli of theta characteristics via Nikulin surfaces
dvi pdf
(with A. Verra) Mathematische Annalen 354 (2012), 465-496
Theta characteristics and their moduli
dvi pdf
Milan Journal of Mathematics 80 (2012), 1-24
The classification of universal Jacobians over the moduli space of curves
dvi pdf
(with A. Verra) To appear in Commentarii Mathematici Helvetici (2012)
Prym varieties and their moduli pdf
Contributions to Algebraic Geometry-IMPANGA Lecture Notes, 215-257
P. Pragacz editor, EMS Congress Reports 2012
Green's Conjecture for general covers
pdf
(with M. Aprodu) Compact moduli spaces and vector bundles-Athens, Georgia 2010
Contemporary Mathematics Vol. 564, 2012, 211-226
Singularities of theta divisors and the geometry of A_5
dvi pdf
(with S. Grushevsky, R. Salvati Manni and A. Verra)
To appear in the Journal of the European Mathematical Society
Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
dvi pdf
(with A. Chiodo, D. Eisenbud and F.-O. Schreyer)
To appear in Inventiones Mathematicae
The universal theta divisor over the moduli space of curves
dvi pdf
(with A. Verra) To appear in Journal de Mathématiques Pures et Appliquées
Effective divisors on moduli spaces of curves
pdf
(with D. Chen and I. Morrison) To appear in "A Celebration of Algebraic Geometry"
Clay Mathematics Proceedings,
Volume published on the occasion of Joe Harris' 60th birthday
Brill-Noether with ramification at unassigned points
dvi pdf
To appear in the Journal of Pure and Applied Algebra
The intermediate type of certain moduli spaces of curves
dvi pdf
(with A. Verra)
The geometry of the moduli space of odd spin curves
dvi pdf
(with A. Verra)
Singularities of the moduli space of level curves
dvi pdf
(with A. Chiodo)
The minimal resolution conjecture and Ulrich bundles
dvi pdf
(with M. Aprodu and A. Ortega)
M_{22} is of general type dvi pdf
Preprint from 2008. Soon to be rewritten and incorporated in "Koszul divisors on moduli spaces of curves II"
Effective divisors on M_g and a counterexample to the Slope Conjecture dvi pdf
(with M. Popa)
The effective cone of M_g and the Slope Conjecture dvi pdf
Max Planck Institute preprint (2003)
This is an extended version of my talk at the
Mathematische Arbeitstagung 2003
Notes on limit linear series for vector bundles on curves dvi pdf
(with M. Popa), unpublished preprint, 2002
Lectures on moduli of curves
Proceedings of the Korean Institute for Mathematical Sciences, Volume 2, No. 1 (2007), 1-20
The birational geometry of the moduli space of curves pdf
Thesis, Universiteit van Amsterdam (2000), book (85 pages), available upon request
A multiplicity theorem in equivariant setting
Mathematica 38 (1996), 221-226
Lusternik-Schnirelmann theory on closed subsets of C^1-manifolds
(with Cs. Varga), Studia Univ. Babes-Bolyai Math. 38 (1993), no. 2, 75-89
On the completeness of Riemanniann manifolds
(with Cs. Varga), Studia Univ. Babes-Bolyai Math. 37 (1992), no. 4, 96-101
PhD Students/Meine Doktoranden
Paul Larsen (PhD 2010), Applied Mori theory of the moduli space of stable pointed rational curves