Prof. Dr. Gavril Farkas

Leiter Lehrstuhl Algebraische Geometrie
Humboldt-Universität zu Berlin
Institut für Mathematik
Rudower Chaussee 25, Raum 1.401
10099 Berlin
Tel: +49 (30) 2093-5412

Sekretariat: Désirée Dzomo Quevedo
Tel: +49 (30) 2093-5823
Fax: +49 (30) 2093-5853

  • Lehre

  • Humboldt Algebraic Geometry Seminar Das Forschungsseminar findet mittwochs von 13:00 Uhr bis 15:00 Uhr in der Rudower Chaussee 25, Raum 3.007 (Haus 3, Erdgeschoss) statt.

    Aktuelles/Upcoming events

  • Brill-Noether Theory, HU Berlin, 5-7 November 2019

  • Moduli in Budapest, a workshop at the Institute of Mathematics of the Hungarian Academy, Budapest 4-6 April 2019

  • Rationality of algebraic varieties, a conference on Schiermonnikoog Island, 15-19 April 2019

  • Varieties, Polyhedra, Computation
    Thematic Einstein Semester on Algebraic Geometry in Berlin, Winter Semester 2019/20. Coorganised with Peter Buergisser and Christian Haase.

  • From January 1st 2015, Rahul Pandharipande is for five years Einstein Visiting Fellow at the Humboldt University

  • Algebraic geometry activities Internationale Tagungen und Forschungsseminare

    Editorial work/Herausgebertätigkeit

  • Algebraic Geometry -Managing Editor

  • Algebra & Number Theory

  • Documenta Mathematica -the Journal of the German Mathematical Society (DMV)

  • EMS Surveys in Mathematical Sciences

  • Mathematica (Cluj) -a publication of the Romanian Academy


    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

  • ERC Advanced Grant SYZYGY: Syzgies, moduli and topological invariants of groups (2020-2024)
    (see also here)

  • DFG Sachbeihilfe Syzygien und Moduli (2018-2020)

  • Berlin Mathematical School-Executive Board member

    Curriculum Vitae: dvi pdf


    The unirationality of the moduli space of K3 surfaces of genus 22 pdf
    (with A. Verra)

    Topological invariants of groups and Koszul modules pdf
    (with M. Aprodu, S. Papadima, C. Raicu and J. Weyman)

    Effective divisors on Hurwitz spaces and moduli of curves pdf

    Alternate Catalan numbers and curves with triple ramification pdf
    (with R. Moschetti, J.C. Naranjo and G.P. Pirola)
    To appear in Annali della Scuola Normale Superiore di Pisa

    Quadric rank loci on moduli of curves and K3 surfaces pdf
    (with R. Rimányi)
    To appear in Annales Scientifiques de L'Ecole Normale Superieure
    Accompanying Macaulay file,

    The uniformization of the moduli space of principally polarized abelian 6-folds pdf
    (with V. Alexeev, R. Donagi, E. Izadi and A. Ortega)
    To appear in the Journal für die reine und angewandte Mathematik

    Koszul modules and Green's Conjecture pdf
    (with M. Aprodu, S. Papadima, C. Raicu and J. Weyman)
    Inventiones Mathematicae 218 (2019), 657-720

    Linear syzygies on curves with prescribed gonality pdf
    (with M. Kemeny)
    Advances in Mathematics 356 (2019), 106810

    The resolution of paracanonical curves of odd genus pdf
    (with M. Kemeny)
    Geometry & Topology 22 (2018), 4235-4257

    Mercat's Conjecture for stable rank 2 vector bundles on generic curves pdf
    (with B. Bakker)
    American Journal of Mathematics 140 (2018), 1277-1295

    The moduli space of twisted canonical differentials pdf
    (with R. Pandharipande)
    Journal of the Institute of Mathematics of Jussieu 17 (2018), 615-672

    The universal K3 surface of genus 14 via cubic fourfolds pdf
    (with A. Verra)
    Journal de Mathématiques Pures et Appliquées 111 (2018), 1-20

    Syzygies of Prym and paracanonical curves of genus 8 pdf
    (with E. Colombo, A. Verra and C. Voisin)
    Épijournal de Géométrie Algébrique 1 (2017)

    Progress on syzygies of algebraic curves pdf
    Lecture Notes of the Unione Matematica Italiana 21 (Moduli of Curves, Guanajuato 2016) 107-138

    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

    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

    Paul Larsen (PhD 2010), Applied Mori theory of the moduli space of stable pointed rational curves
    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
    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

    Current PhD students: Mara Ungureanu (2015-), Irene Schwarz (2016-), Carlos Maestro Perez (2018-)