(see also here)
Direktor des Instituts für Mathematik
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, syzygies of algebraic varieties and commutative algebra aspects, vector bundles on curves, abelian varieties and theta functions, Prym varieties, K3 surfaces and Brill-Noether type problems, geometric group theory and resonance varieties.Current Projects/Laufende Projekte
Publications/Veröffentlichungen
Szegő kernels and Scorza quartics on the moduli space of spin curves pdf
Irrational components of the Hilbert scheme of points
pdf
On the Kodaira dimension of M_16
pdf
The Kodaira dimension of M_22 and
M_23
pdf
Reduced resonance schemes and Chen ranks
pdf
The uniruledness of the Prym moduli space of genus 9
pdf
The Minimal Resolution Property for points on general curves
pdf
Koszul modules with vanishing resonance in algebraic geometry
pdf
Difference varieties and the Green-Lazarsfeld Secant Conjecture
pdf
Higher resonance schemes and Koszul modules of simplicial complexes
pdf
The non-abelian Brill-Noether divisor on M_13 and the Kodaira dimension of R_13
pdf
Linear series on general curves with prescribed incidence conditions
pdf
Generalized de Jonquières divisors on generic curves
pdf
Hodge classes on the moduli space of W(E_6)-covers and the geometry of
A_6
pdf
Topological invariants of groups and Koszul modules
pdf
On the Kodaira dimension of Hurwitz spaces
pdf
Effective divisors on Hurwitz spaces
pdf
The unirationality of the moduli space of K3 surfaces of genus 22
pdf
Alternate Catalan numbers and curves with triple ramification pdf
Quadric rank loci on moduli of curves and K3 surfaces
pdf
The uniformization of the moduli space of principally polarized abelian 6-folds
pdf
Koszul modules and Green's Conjecture
pdf
Linear syzygies on curves with prescribed gonality
pdf
The resolution of paracanonical curves of odd genus
pdf
Mercat's Conjecture for stable rank 2 vector bundles on generic curves
pdf
The moduli space of twisted canonical differentials
pdf
The universal K3 surface of genus 14 via cubic fourfolds
pdf
Syzygies of Prym and paracanonical curves of genus 8
pdf
Progress on syzygies of algebraic curves
pdf
Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces
pdf
The Prym-Green conjecture for torsion line bundles of high order
pdf
Singularities of the moduli space of level curves
pdf
Du Val curves and the pointed Brill-Noether theorem
pdf
Explicit Brill-Noether-Petri general curves
pdf
The universal abelian variety over A_5
dvi pdf
Prym varieties and moduli of polarized Nikulin surfaces
pdf
The generic Green-Lazarsfeld Conjecture
pdf
Pointed Castelnuovo numbers
pdf
Restricted Lazarsfeld-Mukai bundles and canonical curves
pdf
The geometry of the moduli space of odd spin curves
dvi pdf
Singularities of theta divisors and the geometry of A_5
dvi pdf
Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
dvi pdf
The universal theta divisor over the moduli space of curves
dvi pdf
The classification of universal Jacobians over the moduli space of curves
dvi pdf
Brill-Noether with ramification at unassigned points
dvi pdf
Effective divisors on moduli spaces of curves and abelian varieties
pdf
The universal difference variety over the moduli space of curves pdf
Higher rank Brill-Noether theory on sections of K3 surfaces
dvi pdf
Moduli of theta characteristics via Nikulin surfaces
dvi pdf
Theta characteristics and their moduli
dvi pdf
Prym varieties and their moduli pdf
Green's Conjecture for general covers
pdf
Brill-Noether geometry on moduli spaces of spin curves
dvi pdf Koszul cohomology and applications to moduli dvi pdf
The Green Conjecture for smooth curves lying on arbitrary K3 surfaces
dvi pdf
The maximal rank conjecture and rank two Brill-Noether theory
dvi pdf
Aspects of the birational geometry of $\mathcal{M}_g$ dvi
pdf
The birational type of the moduli space of even spin curves dvi pdf The Kodaira dimension of the moduli space of Prym varieties dvi pdf
The Fermat cubic and special Hurwitz loci in the moduli space of curves
dvi pdf
The global geometry of the moduli space of curves
dvi pdf
Gaussian maps, Gieseker-Petri loci and large theta-characteristics
dvi pdf
Effective divisors on M_g, curves on K3 surfaces and the Slope Conjecture dvi pdf
Regular components of moduli spaces of stable maps
dvi pdf
The Mori cones of moduli spaces of pointed curves of small genus
dvi pdf
Divisors on M_{g,g+1} and the minimal resolution conjecture for points on canonical curves
dvi pdf
Brill-Noether loci and the gonality stratification of M_g
dvi pdf
The geometry of the moduli space of curves of genus 23
dvi pdf
Effective divisors on M_g and a counterexample to the Slope Conjecture dvi pdf
The effective cone of M_g and the Slope Conjecture dvi pdf Notes on limit linear series for vector bundles on curves dvi pdf Lectures on moduli of curves
The birational geometry of the moduli space of curves pdf
A multiplicity theorem in equivariant setting
Lusternik-Schnirelmann theory on closed subsets of C^1-manifolds
On the completeness of Riemanniann manifolds
PhD Students/Meine Doktoranden
(with R. Pandharipande and A. Sammartano)
(with A. Verra)
(with D. Jensen and S. Payne)
Notes of my talk on this topic given at ETH in June 2020, to be found here
(with M. Aprodu, C. Raicu and A. Suciu)
Journal für die reine und angewandte Mathematik 814 (2024), 205-240
(with A. Verra)
Advances in Mathematics, Paper no. 109678, (2024)
(with E. Larson)
To appear in the Annales Scientifiques de l'Ecole Normale Superieure
(with M. Aprodu, C. Raicu and J. Weyman)
Selecta Mathematica, article nr. 24, volume 30 (2024)
EPIGA 2024, special issue dedicated to C. Voisin
(with M. Aprodu, C. Raicu, A. Sammartano and A. Suciu)
Journal of Algebraic Combinatorics 59 (2024), 787–805.
(with D. Jensen and S. Payne)
Accompanying Maple file, here.
Geometry & Topology 28 (2024), 803-866
(with C. Lian)
Journal of the Institute of Mathematics of Jussieu 22 (2023), 2857-2877
Studia Univ. Babes-Bolyai Math. 68 (2023), 13-27 (special volume dedicated to the memory of Cs. Varga)
(with V. Alexeev, R. Donagi, E. Izadi and A. Ortega)
Pure and Applied Mathematics Quarterly (Clemens volume) 18 (2022), 1211-1263
(with M. Aprodu, S. Papadima, C. Raicu and J. Weyman)
Duke Mathematical Journal 171 (2022), 2013-2046
(with S. Mullane)
Mathematische Zeitschrift 300 (2022), 3417-3432 (special volume dedicated to O. Debarre)
Facets of Algebraic Geometry (LMS Lecture Notes Series 472), Vol. 1, 221-240, a volume in honor of Fulton's 80th birthday
(with A. Verra)
Mathematische Annalen 380 (2021), 953-973
(with R. Moschetti, J.C. Naranjo and G.P. Pirola)
Annali della Scuola Normale Superiore di Pisa 22 (2021), 665-690
(with R. Rimányi)
Annales Scientifiques de L'Ecole Normale Superieure 53 (2020), 945-992
Accompanying Macaulay file, here.
(with V. Alexeev, R. Donagi, E. Izadi and A. Ortega)
Journal für die reine und angewandte Mathematik 761 (2020), 163-217
(with M. Aprodu, S. Papadima, C. Raicu and J. Weyman)
Inventiones Mathematicae 218 (2019), 657-720
(with M. Kemeny)
Advances in Mathematics 356 (2019), 106810
(with M. Kemeny)
Geometry & Topology 22 (2018), 4235-4257
(with B. Bakker)
American Journal of Mathematics 140 (2018), 1277-1295
(with R. Pandharipande)
Journal of the Institute of Mathematics of Jussieu 17 (2018), 615-672
(with A. Verra)
Journal de Mathématiques Pures et Appliquées 111 (2018), 1-20
(with E. Colombo, A. Verra and C. Voisin)
Épijournal de Géométrie Algébrique 1 (2017)
Lecture Notes of the Unione Matematica Italiana 21 (Moduli of Curves, Guanajuato 2016) 107-138
(with M. Aprodu and A. Ortega)
Journal für die reine und angewandte Mathematik 730 (2017), 225-249
(with M. Kemeny)
Duke Mathematical Journal 166 (2017), 1103-1124
(with A. Chiodo)
Journal of the European Mathematical Society 19 (2017), 603-658
(with N. Tarasca)
Selecta Mathematica 23 (2017), 2243-2259
(with E. Arbarello, A. Bruno and G. Sacca)
Commentarii Mathematici Helvetici 91(2016), 477-491
(with A. Verra)
Annales Scientifiques de L'Ecole Normale Superieure 49 (2016), 521-543
(with A. Verra)
Advances in Mathematics 290 (2016), 314-328
(with M. Kemeny)
Inventiones Mathematicae 203 (2016), 265-301
(with N. Tarasca) Mathematical Research Letters 23 (2016), 389-404
(with M. Aprodu and A. Ortega), Development of Moduli Theory (Kyoto 2013)
Advanced Studies in Pure Mathematics 69 (2016), 303-322.
(with A. Verra)
Annals of Mathematics 180 (2014), 927-970
(with S. Grushevsky, R. Salvati Manni and A. Verra)
Journal of the European Mathematical Society 16 (2014),
1817-1848
(with A. Chiodo, D. Eisenbud and F.-O. Schreyer)
Inventiones Mathematicae 194 (2013), 73-118
(with A. Verra)
Journal de Mathématiques Pures et Appliquées 100 (2013), 591-605
(with A. Verra)
Commentarii Mathematici Helvetici 88 (2013), 587-611
Journal of Pure and Applied Algebra 217(2013), 1838-1843
(with D. Chen and I. Morrison) A Celebration of Algebraic Geometry 131-169
Clay Mathematics Proceedings, B. Hassett, J. McKernan, J. Starr, R. Vakil editors, Volume 18, 2013
(with A. Verra) Rendiconti del Circolo Matematico di Palermo 62 (2013), 97-110
(with A. Ortega)
International Journal of Mathematics 23 (2012) 1250075
(with A. Verra)
Mathematische Annalen 354 (2012), 465-496
Milan Journal of Mathematics 80 (2012), 1-24
Contributions to Algebraic Geometry-IMPANGA Lecture Notes, 215-257
P. Pragacz editor, EMS Congress Reports 2012
(with M. Aprodu) Compact moduli spaces and vector bundles-Athens, Georgia 2010
Contemporary Mathematics Vol. 564, 2012, 211-226
Classification of algebraic varieties-Schiermonnikoog 2009, 259-276
C. Faber, G. van der Geer, E. Looijenga editors, EMS Congress Reports 2011
(with M. Aprodu)
Grassmannians, moduli spaces and vector bundles
Clay Mathematics Proceedings, E. Previato editor, Volume 14, 2011, 25-50
(with M. Aprodu)
Compositio Mathematica 147 (2011), 839-851
(with A. Ortega)
Pure and Applied Mathematics Quarterly 7 (2011), 1265-1296
"Geometry of Riemann surfaces and their moduli spaces"
Surveys in Differential Geometry Vol. 14 (2010), 57-111
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
(with K. Ludwig) Journal of the European Mathematical Society 12 (2010), 755-795
Bulletin of the Belgian Mathematical Society "Simon Stevin" 5 (2009), 831-851
Special volume dedicated to the conference "Linear series and subschemes"-Ghent 2007
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 intermediate type of certain moduli spaces of curves
dvi pdf
(with A. Verra), preprint from 2009
Journal of the London Mathematical Society 78 (2008), 418-440
Duke Mathematical Journal 135 (2006), 53-98
J. reine angewandte Mathematik 581 (2005), 151-174
(with M. Popa)
Journal of Algebraic Geometry 14 (2005), 241-267
Proceedings of the American Mathematical Society 131 (2003), 2027-2036
(with A. Gibney),
Transactions of the American Mathematical Society 355 (2003), 1183-1199
(with M. Mustata and M. Popa), Annales Scientifiques de L'Ecole Normale Superieure 36 (2003), 553-581
J. reine angewandte Mathematik 539 (2001), 185-200
Mathematische Annalen 318 (2000), 43-65
(with M. Popa)
Max Planck Institute preprint (2003)
This is an extended version of my talk at the
Mathematische Arbeitstagung 2003 (Bonn)
(with M. Popa), unpublished preprint, 2002
Proceedings of the Korean Institute for Mathematical Sciences, Volume 2, No. 1 (2007), 1-20
Thesis, Universiteit van Amsterdam (2000), book (85 pages), available upon request
(with Cs. Varga) Mathematica 38 (1996), 221-226
(with Cs. Varga) Studia Univ. Babes-Bolyai Math. 38 (1993), no. 2, 75-89
(with Cs. Varga) Studia Univ. Babes-Bolyai Math. 37 (1992), no. 4, 96-101
My papers reviewed on MathSciNet
Nicola Tarasca (PhD 2012), Geometric cycles on the moduli space of curves
Margherita Lelli-Chiesa (PhD 2012), Gieseker-Petri divisors and Brill-Noether theory of K3 sections-Mario Baldassari Prize 2015
Fabian Müller (PhD 2013), Effective divisors on moduli spaces of pointed stable curves
Arie Peterson (PhD 2015), Modular forms on the moduli space of polarized K3 surfaces
Gregor Bruns (PhD 2016), Divisors on moduli spaces of level curves
Emre Sertöz (PhD 2017), Enumerative geometry of double spin curves
Irfan Kadiköylu (PhD 2018), Rank stratifications of spaces of quadrics and moduli of curves
Daniele Agostini (PhD 2018), On syzygies of algberaic varieties with applications to moduli
Ignacio Barros (PhD 2018), K3 surfaces and moduli of holomorphic differentials
Mara Ungureanu (PhD 2018), Enumerative formulas of de Jonquieres type on algebraic curves
Irene Schwarz (PhD 2020), Birational geometry of moduli spaces of pointed curves
Carlos Maestro Perez (PhD 2021), Aspects of the geometry of Prym varieties and their moduli
Andrei Bud (PhD 2022), Moduli of Prym curves and strata of differentials - MATH+ Dissertation Award 2024 and Finalist of the Adlershofer Dissertationspreis 2023
Federico Moretti (PhD 2024), Variational aspects of curves and K3 surfaces
Current PhD students: Li Li (2021-), Vincent Ariksoy (2024-), Riccardo Redigolo (2025-)