Scientific Publications

Refereed Papers

Submitted for publication

2017 Klt varieties with trivial canonical class – Holonomy, differential forms, and fundamental groups (with Daniel Greb and Henri Guenancia)
Preprint arXiv:1704.01408.
2015 The Miyaoka-Yau inequality and uniformisation of canonical models (with Daniel Greb, Thomas Peternell and Behrouz Taji)
Preprint arXiv:1511.08822.

Accepted for publication

2016 Survey paper: Generic positivity and applications to hyperbolicity of moduli spaces (with Benoît Claudon and Behrouz Taji)
to appear as a chapter of a book about complex hyperbolicity.
Preprint arXiv:1610.09832.
Survey paper: Uniformisation of higher-dimensional varieties (with Daniel Greb and Behrouz Taji)
to appear in “Proceedings of 2015 Summer Institute on Algebraic Geometry”, Proceedings of Symposia in Pure Mathematics.
Preprint arXiv:1608.06644.
Differential forms in positive characteristic avoiding resolution of singularities (with Annette Huber and Shane Kelly)
To appear in Bulletin de la Société Mathématique de France.
Preprint arXiv:1407.5786.
2014 Comparing $\mathbb A^1$-$h$-cobordism and $\mathbb A^1$-weak equivalence (with Aravind Asok and Matthias Wendt)
To appear in: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
Preprint arXiv:1410.3038.


2016 Singular spaces with trivial canonical class (with Daniel Greb und Thomas Peternell).
in “Minimal Models and Extremal Rays (Kyoto, 2011)”. Advanced Studies in Pure Mathematics 70, Pages 67-113, Mathematical Society of Japan, Tokyo, 2016.
Preprint arXiv:1110.5250.
Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties (with Daniel Greb und Thomas Peternell).
Duke Math. J., Volume 165, Number 10 (2016), 1965-2004. DOI:10.1215/00127094-3450859. Preprint arXiv:1307.5718.
Survey paper: Aspects of the geometry of varieties with canonical singularities (with Thomas Peternell)
Simons Symposia: Foliation Theory in Algebraic Geometry, Editors: Paolo Cascini, James McKernan and Jorge Vitório Pereira. Springer, New York, 2016.
DOI:10.1007/978-3-319-24460-0. Available from this URL.
Movable curves and semistable sheaves (with Daniel Greb and Thomas Peternell).
Int Math Res Notices, 2016 (2): 536-570. DOI:10.1093/imrn/rnv126. Preprint arXiv:1408.4308 contains an extended version with additional figures.
2014 Reflexive differential forms on singular spaces — Geometry and Cohomology (with Daniel Greb and Thomas Peternell).
Journal für die reine und angewandte Mathematik (Crelles Journal). Vol 697, pp 57–89 (2014).
DOI:10.1515/crelle-2012-0097. Preprint arXiv:1202.3243.
2013 Pull-back morphisms for reflexive differential forms
Advances in Mathematics, Volume 245, pp. 78-112, 2013.
DOI:10.1016/j.aim.2013.06.013. Preprint arXiv:1210.3255.
Survey paper: Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacks
In: Handbook of Moduli, Volume II, Editors: Gavril Farkas and Ian Morrison. Number 26 in Advanced Lectures in Mathematics, International Press, Beijing
Preprint arXiv:1107.4239.
Survey paper: Uniruledness criteria and applications,
In: Simons Symposia: Birational Geometry, Rational Curves, and Arithmetic, Editors: Fedor Bogomolov, Brendan Hassett and Yuri Tschinkel, pp. 147-162, Springer, New York, 2013.
DOI:10.1007/978-1-4614-6482-2. Available from this URL.
2012 Deformations along subsheaves, II (with Clemens Jörder)
EMS Series of Congress Reports, Contributions of Algebraic Geometry, Impanga Lecture Notes (Trends in Mathematics), EMS Publishing House, 2012.
DOI:10.4171/114. Preprint arXiv:1103.5630.
2011 Positive sheaves of differentials coming from coarse moduli spaces (with Kelly Jabbusch)
Annales de l’institut Fourier, 61 no. 6 (2011), p. 2277-2290,
DOI:10.5802/aif.2673. Preprint arXiv:0904.2445.
Differential Forms on Log Canonical Spaces (with Daniel Greb, Sándor Kovács and Thomas Peternell)
Publications Mathématiques de l’IHÉS, Volume 114, Number 1 (2011), 87-169.
DOI:10.1007/s10240-011-0036-0. Preprint arXiv:1003.2913 contains an extended version with additional graphics.
Families over special base manifolds and a conjecture of Campana (with Kelly Jabbusch)
Mathematische Zeitschrift: Volume 269, Issue 3 (2011), Page 847-878.
DOI:10.1007/s00209-010-0758-6. Preprint arXiv:0905.1746.
Deformations along subsheaves (with Stavros Kousidis and Daniel Lohmann)
L’Enseignement Mathématique, Vol. 56, pp. 287-313, 2010.
DOI:10.4171/LEM/56-3-3. Preprint arXiv:0905.2749.
2010 The structure of surfaces and threefolds mapping to the moduli stack of canonically polarized manifolds (with Sándor Kovács)
Duke Mathematical Journal, Vol. 155, No 1, pp. 1-33, 2010.
DOI:10.1215/00127094-2010-049. Preprint arXiv:0812.2305.
Extension theorems for differential forms and Bogomolov-Sommese vanishing on log canonical varieties (with Daniel Greb and Sándor Kovács)
Compositio Mathematica, Vol. 146, pp. 193–219, 2010.
DOI:10.1112/S0010437X09004321. Preprint arXiv:0808.3647.
2008 A refinement of Stein factorization and deformations of surjective morphisms (with Thomas Peternell)
Asian Journal of Mathematics, Vol. 12, No. 3, pp. 365-389, 2008.
DOI:10.4310/AJM.2008.v12.n3.a6. Preprint arXiv:math/0508285.
Families of varieties of general type over compact bases (with Sándor Kovács)
Advances in Mathematics, Vol. 218, No. 3, pp. 649-652, 2008.
DOI:10.1016/j.aim.2008.01.005. Preprint arXiv:math/0511378.
Families of canonically polarized varieties over surfaces (with Sándor Kovács)
Inventiones Mathematicae, Vol. 172, No. 3, pp. 657-682, 2008.
DOI:10.1007/s00222-008-0128-8. Preprint arXiv:math/0511378.
Galois coverings and endomorphisms of projective varieties (with Marian Aprodu and Thomas Peternell)
Mathematische Zeitschrift,  Vol. 260, No. 2, pp. 431-449, 2008.
DOI:10.1007/s00209-007-0282-5. Preprint arXiv:arXiv:0705.4602.
2007 Rationally connected foliations after Bogomolov and McQuillan (with Luis Solá and Matei Toma)
Journal Algebraic Geometry, Vol. 16, No. 1, pp. 65-81, 2007.
DOI:10.1090/S1056-3911-06-00435-8. Preprint arXiv:math/0505222.
2006 Existence of rational curves on algebraic varieties, minimal rational tangents, and applications (with Luis Solá)
In Global Aspects of Complex Geometry, pp. 359-416. Springer, 2006
DOI:10.1007/3-540-35480-8_10. Preprint arXiv:math/0512487.
Holomorphic maps onto varieties of non-negative Kodaira dimension (with Jun-Muk Hwang and Thomas Peternell)
Journal of Algebraic Geometry, Vol. 15, pp. 551-561, 2006.
DOI:10.1090/S1056-3911-05-00411-X. Preprint arXiv:math/0307220.
2005 Geometry of chains of minimal rational curves (with Jun-Muk Hwang)
Journal für die reine und angewandte Mathematik, Vol. 584, pp. 173-194, 2005.
DOI:10.1515/crll.2005.2005.584.173. Preprint arXiv:math/0403352.
Lines on complex contact manifolds, II
Compositio Mathematica, Vol. 141, No. 1, pp. 227-252, 2005.
DOI:10.1112/S0010437X04000880. Preprint arXiv:math/0306260.
2004 Are minimal degree rational curves determined by their tangent vectors? (with Sándor Kovács)
Annales de l’Institut Fourier, Vol. 54, No. 1, pp. 53-80, 2004.
Available from this URL. Preprint arXiv:math/0206193.
2002 Projective bundles of singular plane cubics
Mathematische Nachrichten, Vol. 242, No. 1, pp. 119-131, 2002.
DOI:10.1002/1522-2616(200207)242:13.0.CO;2-R. Preprint arXiv:math/0009083.
Characterizing the projective space after Cho, Miyaoka and Shepherd-Barron
In Complex Geometry, Collection of Papers dedicated to Hans Grauert, pp. 147-156. Springer, 2002.
Preprint arXiv:math/0107069.
A reduction map for NEF line bundles (with Thomas Bauer, Frédéric Campana, Thomas Eckl, Thomas Peternell, Sławomir Rams, Tomasz Szemberg and Lorenz Wotzlaw)
In Complex Geometry, Collection of Papers dedicated to Hans Grauert, pp. 27-36. Springer, 2002.
Preprint arXiv:math/0106147.
Manifolds with nef rank 1 subsheaves in $\Omega^1_X$ (with Thomas Peternell and Andrew J. Sommese)
In Complex Geometry, Collection of Papers dedicated to Hans Grauert, pp. 157-164. Springer, 2002.
Families of singular rational curves
Journal of Algebraic Geometry, Vol. 11, pp. 245-256, 2002.
DOI:10.1090/S1056-3911-01-00308-3. Preprint arXiv:math/0004023.
2001 Lines on contact manifolds
Journal für die reine und angewandte Mathematik, Vol. 539, pp. 167-177, 2001.
DOI:10.1515/crll.2001.072. Preprint arXiv:math/0004103.
2000 Projective Contact Manifolds  (with Thomas Peternell, Andrew J. Sommese and Jarosław A. Wiśniewski)
Inventiones Mathematicae, Vol. 142, No. 1, pp. 1-15, 2000.
DOI:10.1007/PL00005791. Preprint arXiv:math/9810102.
Group Actions on $S^6$ and complex structures on $\mathbb P_3(\mathbb C)$ (with Alan T. Huckleberry and Thomas Peternell)
Duke Mathematical Journal, Vol. 102, No. 1, pp. 101-124, 2000.
DOI:10.1215/S0012-7094-00-10214-1. Preprint arXiv:math/9812076.
On the Classification of 3-dimensional $\operatorname{SL}_2(\mathbb C)$-varieties
Nagoya Mathematical Journal, Vol. 157, pp. 129-147, 2000.
Available from this URL. Preprint arXiv:math/9805043.
Relatively Minimal Quasihomogeneous Projective 3-Folds
Nagoya Mathematical Journal, Vol. 157, pp. 149-176, 2000.
Available from this URL. Preprint arXiv:math/9805042.
1998 Simple Models of Quasihomogeneous Projective 3-Folds
Documenta Mathematica, Vol. 3, pp. 15-26, 1998.
Preprint arXiv:math/9805041.

Non-refereed papers

2004 Survey paper: Holomorphe Abbildungen auf Mannigfaltigkeiten mit nicht-negativer Kodaira-Dimension (German)
Mathematisches Institut, Seminars, Ed.: Y. Tschinkel, Universität Göttingen, pp. 157-166, 2004.
Available from this URL.
2000 Survey paper: Bounds for Families of Singular Rational Curves
Conference proceedings of the Saitama Conference in Algebraic Geometrye, Saitama University, Urawa City (Japan), 2000.
Available from this URL.

Other publications

2013 Moduli spaces in algebraic geometry
Abstracts from the workshop held February 3–9, 2013. Organized by Dan Abramovich, Lucia Caporaso, Gavril Farkas and Stefan Kebekus.
Oberwolfach Rep. 10 (2013), no. 1, 343–392.
2010 Moduli spaces in algebraic geometry
Abstracts from the workshop held January 10–16, 2010. Organized by Dan Abramovich, Gavril Farkas and Stefan Kebekus. Oberwolfach Reports. Vol. 7, no. 1.
Oberwolfach Rep. 7 (2010), no. 1, 55–107.
2009 Multiplier ideal sheaves in algebraic and complex geometry
Abstracts from the workshop held April 12–18, 2009. Organized by Stefan Kebekus, Mihai Paun, Georg Schumacher and Yum-Tong Siu. Oberwolfach Reports. Vol. 6, no. 2.
Oberwolfach Rep. 6 (2009), no. 2, 1101–1155.

Ph.D. thesis and Habilitation

2001 Rationale Kurven auf projektiven Mannigfaltigkeiten (German)
Habilitationsschrift, Universität Bayreuth, 2001.
Available from this URL.
1996 Almost Homogeneous Projective 3-Folds
Ph.D. thesis, Ruhr-Universität Bochum, 1996.
Available from this URL.