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: Jutta Mögle
Tel: +49 (30) 2093-5823
Fax: +49 (30) 2093-5853

  • Lehre

  • Humboldt Algebraic Geometry Seminar Das Forschungsseminar findet mittwochs von 15:00 Uhr bis 17:00 Uhr in der Rudower Chaussee 25, Raum 2.009 (Haus 2, Erdgeschoss) statt.

    Aktuelles/Upcoming events

  • A Day of algebraic and arithmetic geometry, Berlin -Brandenburgische Akademie der Wissenschaften May 20, 2016

  • Geometry of algebraic varieties, Berlin, October 6-9, 2015. A conference on the occasion of Sandro Verra's 65th birthday

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

  • Algebraic geometry activities Internationale Tagungen und Forschungsseminare

    Editorial work/Herausgebertätigkeit

  • Algebraic Geometry

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

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

  • The Handbook of Moduli Volumes I-III, coedited with Ian Morrison, a vast survey of moduli theory


    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

  • DFG Sonderforschungsbereich 647 Raum-Zeit_Materie. Analytische und Geometrische Strukturen -project leader
  • DFG Schwerpunkt 1489 Algorithmische und Experimentelle Methoden in Algebra, Geometrie und Zahlentheorie -project leader
  • International Research Training Group GRK 1800 Moduli and automorphic forms: Arithmetic and Geometric Aspects (Berlin-Amsterdam-Leiden)- principal investigator
  • Berlin Mathematical School-Executive Board member

    Curriculum Vitae: dvi pdf


    Mercat's Conjecture for stable rank 2 vector bundles on generic curves pdf
    (with B. Bakker)

    The Prym-Green conjecture for torsion line bundles of high order pdf
    (with M. Kemeny)

    The uniformization of the moduli space of principally polarized abelian 6-folds pdf
    (with V. Alexeev, R. Donagi, E. Izadi and A. Ortega)

    Explicit Brill-Noether-Petri general curves pdf
    (with E. Arbarello, A. Bruno and G. Sacca)
    To appear in Commentarii Mathematici Helvetici

    The moduli space of twisted canonical differentials pdf
    (with R. Pandharipande)
    To appear in the Journal of the Institute of Mathematics of Jussieu

    The universal abelian variety over A_5 dvi pdf
    (with A. Verra)
    To appear in Annales Scientifiques de L'Ecole Normale Superieure

    Pointed Castelnuovo numbers pdf
    (with N. Tarasca) To appear in Mathematical Research Letters

    Singularities of the moduli space of level curves pdf
    (with A. Chiodo) To appear in the Journal of the European Mathematical Society

    Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces pdf
    (with M. Aprodu and A. Ortega)
    To appear in the Journal für die reine und angewandte Mathematik

    Restricted Lazarsfeld-Mukai bundles and canonical curves pdf
    (with M. Aprodu and A. Ortega)
    To appear in Advanced Studies in Pure Mathematics (Math. Soc. Japan) on the occasion of Mukai's 60th birthday

    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

    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

    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
    Fabian Müller (PhD 2013), Effective divisors on moduli spaces of pointed stable curves

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