Leiter Lehrstuhl Algebraische Geometrie

Humboldt-Universität zu Berlin

Institut für Mathematik

Rudower Chaussee 25, Raum 1.401

10099 Berlin

Tel: +49 (30) 2093-5412

e-mail: farkas-at-math.hu-berlin.de

Sekretariat: Kristina Schulze

Tel: +49 (30) 2093-5823

Fax: +49 (30) 2093-5853

e-mail: schulze-at-math.hu-berlin.de

** Aktuelles/Upcoming events**

**Editorial work/Herausgebertätigkeit**

**Research/Forschungsgebiet**

**Current Projects/Laufende Projekte**

**Publications/Veröffentlichungen**

(with R. Rimányi)

*The resolution of paracanonical curves of odd genus*
pdf

(with M. Kemeny)

*Linear syzygies on curves with prescribed gonality*
pdf

(with M. Kemeny)

*Progress on syzygies of algebraic curves*
pdf

To appear in the Proceedings of the CIMPA-CIMAT-ICTP School on Moduli of Curves, 2016 (Lecture Notes in Mathematics)

*The universal K3 surface of genus 14 via cubic fourfolds*
pdf

(with A. Verra) To appear in the Journal de Mathématiques Pures et Appliquées

*The uniformization of the moduli space of principally polarized abelian 6-folds*
pdf

(with V. Alexeev, R. Donagi, E. Izadi and A. Ortega)

*Mercat's Conjecture for stable rank 2 vector bundles on generic curves*
pdf

(with B. Bakker) To appear in the American Journal of Mathematics

*The moduli space of twisted canonical differentials*
pdf

(with R. Pandharipande)

To appear in the Journal of the Institute of Mathematics of Jussieu

*Syzygies of Prym and paracanonical curves of genus 8*
pdf

(with E. Colombo, A. Verra and C. Voisin)

Épijournal de Géométrie Algébrique 1 (2017)

*Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces*
pdf

(with M. Aprodu and A. Ortega)

Journal für die reine und angewandte Mathematik 730 (2017), 225-249

*The Prym-Green conjecture for torsion line bundles of high order*
pdf

(with M. Kemeny)

Duke Mathematical Journal 166 (2017), 1103-1124

*Singularities of the moduli space of level curves*
pdf

(with A. Chiodo)

Journal of the European Mathematical Society 19 (2017), 603-658

*Du Val curves and the pointed Brill-Noether theorem*
pdf

(with N. Tarasca)

Selecta Mathematica 23 (2017), 2243-2259

*Explicit Brill-Noether-Petri general curves*
pdf

(with E. Arbarello, A. Bruno and G. Sacca)

Commentarii Mathematici Helvetici 91(2016), 477-491

*The universal abelian variety over A_5*
dvi pdf

(with A. Verra)

Annales Scientifiques de L'Ecole Normale Superieure 49(2016), 521-543

*Prym varieties and moduli of polarized Nikulin surfaces*
pdf

(with A. Verra)

Advances in Mathematics 290 (2016), 314-328

*The generic Green-Lazarsfeld Conjecture*
pdf

(with M. Kemeny)

Inventiones Mathematicae 203 (2016), 265-301

*Pointed Castelnuovo numbers*
pdf

(with N. Tarasca) Mathematical Research Letters 23(2016), 389-404

*Restricted Lazarsfeld-Mukai bundles and canonical curves*
pdf

(with M. Aprodu and A. Ortega), Development of Moduli Theory (Kyoto 2013)

Advanced Studies in Pure Mathematics 69 (2016), 303-322.

*The geometry of the moduli space of odd spin curves*
dvi pdf

(with A. Verra)

Annals of Mathematics 180 (2014), 927-970

*Singularities of theta divisors and the geometry of A_5*
dvi pdf

(with S. Grushevsky, R. Salvati Manni and A. Verra)

Journal of the European Mathematical Society 16 (2014),
1817-1848

*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)

Inventiones Mathematicae 194 (2013), 73-118

* The universal theta divisor over the moduli space of curves*
dvi pdf

(with A. Verra)

Journal de Mathématiques Pures et Appliquées 100 (2013), 591-605

* The classification of universal Jacobians over the moduli space of curves*
dvi pdf

(with A. Verra)

Commentarii Mathematici Helvetici 88 (2013), 587-611

*Brill-Noether with ramification at unassigned points*
dvi pdf

Journal of Pure and Applied Algebra 217(2013), 1838-1843

*Effective divisors on moduli spaces of curves and abelian varieties*
pdf

(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

* The universal difference variety over M_g* pdf

(with A. Verra) Rendiconti del Circolo Matematico di Palermo 62 (2013), 97-110

* 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

*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

*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

*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

*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

*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 intermediate type of certain moduli spaces of curves*
dvi pdf

(with A. Verra), preprint from 2009

* Higher ramification and varieties of secant divisors on the generic curve
* dvi pdf

Journal of the London Mathematical Society 78 (2008), 418-440

*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"

* Syzygies of curves and the effective cone of M_g* dvi pdf

Duke Mathematical Journal 135(2006), 53-98

* 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

*Regular components of moduli spaces of stable maps*
dvi pdf

Proceedings of the American Mathematical Society 131 (2003), 2027-2036

*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

*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

*Brill-Noether loci and the gonality stratification of M_g *
dvi pdf

J. reine angewandte Mathematik 539 (2001), 185-200

*The geometry of the moduli space of curves of genus 23*
dvi pdf

Mathematische Annalen 318 (2000), 43-65

*
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*

(with Cs. Varga) 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

My papers reviewed on MathSciNet

**PhD Students/Meine Doktoranden**

Nicola Tarasca (PhD 2012),

Margherita Lelli-Chiesa (PhD 2012),

Fabian Müller (PhD 2013),

Gregor Bruns (PhD 2016),

Current PhD students: Emre Sertöz (2013-2016), Daniele Agostini (2014-2017), Irfan Kadiköylu (2013-2016), Ignacio Barros (2014-2017), Mara Ungureanu (2015-18), Irene Schwarz (2016-19)