Professor of Mathematics
During the Fall of 2011 I am on sabbatical at the Universita Roma Tre. For this reason, the HU Algebraic Geometry Seminar will only meet irregularly.
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 and Gromov-Witten theory, vector bundles on curves, abelian varieties and theta functions, Prym varieties, K3 surfaces, Brill-Noether type problems and syzygies of algebraic varieties.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 American Mathematical Society 355 (2003), 1183-1199
Regular components of moduli spaces of stable maps
dvi pdf
Proceedings 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.
The classification of universal Jacobians over the moduli space of curves
dvi pdf
(with A. Verra) To appear in Commentarii Mathematici Helvetici (2012)
Moduli of theta characteristics via Nikulin surfaces
dvi pdf
(with A. Verra) To appear in Mathematische Annalen (2012)
Higher rank Brill-Noether theory on sections of K3 surfaces
dvi pdf
(with A. Ortega) To appear in the International Journal of Mathematics (2012)
Prym varieties and their moduli pdf
To appear in "Contributions to Algebraic Geometry" (P. Pragacz editor), Impanga Lecture Notes, published by the EMS
Green's Conjecture for general covers
pdf
(with M. Aprodu) To appear in "Vector bundles and compact moduli-Athens, Georgia 2010", Contemporary Mathematics 2012
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)
The universal theta divisor over the moduli space of curves
dvi pdf
(with A. Verra)
Singularities of theta divisors and the geometry of A_5
dvi pdf
(with S. Grushevsky, R. Salvati Manni and A. Verra)
Theta characteristics and their moduli
dvi pdf
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