Publications and Preprints


    1. Motives of isogenous K3 surfaces. 12 pages. to appear in Commentarii Mathematici Helvetici. arXiv:1705.04063

    2. Motives of derived equivalent K3 surfaces. 7 pages. to appear in Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg. arXiv:1702.03178

    3. (with J. Rennemo) Hochschild cohomology versus the Jacobian ring, and the Torelli theorem for cubic fourfolds. 27 pages. to appear in Algebraic Geometry arXiv:1610.04128

    4. The K3 category of a cubic fourfold. Compositio Mathematica 153 (2017), 586-620 arXiv:1505.01775

    5. On derived categories of K3 surfaces and Mathieu groups. 16 pages. Advanced Studies in Pure Math. 69 (Math. Soc. Japan) 2016 arXiv:1309.6528

    6. (with an appendix by C. Voisin) Curves and cycles on K3 surfaces. Algebraic Geometry 1 (2014), 69-106. arXiv:1303.4564

    7. Symplectic automorphisms of K3 surfaces of arbitrary order. Math. Res. Lett. 19 (2012), 947-951. arXiv:1205.3433v1

    8. (with M. Kemeny) Stable maps and Chow groups. Documenta mathematica 18 (2013), 507-517. arXiv:1202.4968

    9. Introduction to stability conditions. in 'Moduli Spaces' Cambridge University Press edited by Brambila Paz, Newstead, Thomas and Garcia-Prada Lectures at the Newton Institute January 2011. 47 pages. arXiv:1111.1745v1

    10. A Global Torelli theorem for hyperkähler manifolds (after Verbitsky). Seminaire Bourbaki Exp. No. 1040 Juin 2011 Astérisque No. 348 (2012), 375-403. arxiv:1106.5573

    11. Stability conditions via spherical objects. Math. Z. 271 (2012), no. 3-4, 1253-1270. arXiv:1009.4372

    12. A note on the Bloch-Beilinson conjecture for K3 surfaces and spherical objects. Pure Appl. Math. Q. 7 (2011), no. 4, Special Issue: In memory of Eckart Viehweg, 1395-1405 arXiv:1009.4371

    13. Hyperkähler manifolds and sheaves. Proceedings of the International Congress of Mathematicians. Volume II,450-460. pdf-file

    14. Chow groups and derived categories of K3 surfaces. 16 pages. Current developments in algebraic geometry, 177-195, Math. Sci. Res. Inst. Publ., 59. arXiv:0912.5299v1

    15. (with E. Macri, P. Stellari) Formal deformations and their categorical general fibre. Comment. Math. Helv. 86 (2011), 41-71 This is Part one of arXiv:0710.1645v2. arXiv:0809.3201v1

    16. (with E. Macri, P. Stellari) Derived equivalences of K3 surfaces and orientation. Duke Math. J. 149 (2009), 461-507. This is Part two of arXiv:0710.1645v2. arXiv:0710.1645v3

    17. Chow groups of K3 surfaces and spherical objects. Journal EMS 12 (2010), 1533-1551. arXiv:0809.2606v1

    18. (with R. Thomas) Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes. Math. Ann. 346 (2010), 545-569. arXiv:0805.3527v1

    19. (with M. Nieper-Wisskirchen) Remarks on derived equivalences of Ricci-flat manifolds. Math. Zeit. 267 (2011), 939-963. arXiv:0801.4747.

    20. (with E. Macri, P. Stellari) Derived equivalences of K3 surfaces and orientation. 70 pages. arXiv:0710.1645v2

    21. (with E. Macri, P. Stellari) Stability conditions for generic K3 categories. 32 pages. Comp. math. 144 (2008), 134-162. math.AG/0608430

    22. Derived and abelian equivalence of K3 surface. J. Alg. Geom. 17 (2008), 375-400. math.AG/0604150

    23. The global Torelli theorem: classical, derived, twisted. Algebraic geometry-Seattle 2005. Part 1, 235-258, Proc. Sympos. Pure Math., 80, Part 1, Amer. Math. Soc., Providence, RI, 2009. arXiv:math/0609017v1 (2006). published version slightly different.

    24. (with R. Thomas) P-objects and autoequivalences of derived categories. MRL 13 (2006), 87-98. math.AG/0507040

    25. Projectivity of Kähler manifolds - Kodaira's problem (after C. Voisin) Astérisque No. 311 (2007), Exp. No. 954, vii, 55-73. Seminaire Bourbaki math.AG/0512039

    26. (with P. Stellari) Proof of Caldararu's conjecture. Adv. Stud. Pure Math. 45. 'Moduli spaces and arithmetic of algebraic varieties.' (2007), 31-42. math.AG/0411541

    27. (with P. Stellari) Equivalences of twisted K3 surfaces. Math. Ann. 332 (2005), 901-936. math.AG/0409030

    28. Generalized Calabi-Yau structures, K3 surfaces, and B-fields. Int. J. Math. 16 (2005), 13-36. math.AG/0306162

    29. (with S. Schroeer) The Brauer group of analytic K3 surfaces. IMRN. 50 (2003), 2687-2698. math.AG/0305101

    30. Moduli spaces of hyperkähler manifolds and mirror symmetry. Intersection theory and moduli, 185-247 (electronic), ICTP Lect. Notes, XIX, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004. math.AG/0210219

    31.  Finitenes results for hyperkähler manifolds. J. reine angew. Math. 558 (2003), 15-22. math.AG/0109024

    32. The Kähler cone of a compact hyperkähler manifold. completely revised version of the 1999 preprint.Math. Ann. 326 (2003), 499-513. math.AG/9909109

    33. Erratum to the paper: Compact hyperkähler manifolds: basic results. Invent. math. 152 (2003), 209-212. math.AG/0106014

    34. Product of harmonic forms and rational curves. Documenta Mathematica 6 (2001), 227-239. math/0003202

    35. Compact hyperkähler manifolds: Basic results. Invent. Math. 135 (1999), 63-113. alg-geom/9705025

    36. Compact hyperkähler manifolds. Habilitationsschrift Essen (1997), 65 pages ( ps-file )

    37. Birational symplectic manifolds and their deformations. J. Diff. Geom. 45 (1997), 488-513. alg-geom/9601015

    38. (with L. Göttsche) - Hodge numbers of moduli spaces of stable sheaves on K3 surfaces. Int. J. Math. 7 (1996), 359-372. alg-geom/9408001

    39. The tangent bundle of a Calabi-Yau manifold - Deformations and restrictions to rational curves. Comm. Math. Phys. 171 (1995), 139-158. ( ps-file )

    40. (with M. Lehn) Framed modules and their moduli. Int. J. Math. 6 (1995), 297-324. ( ps-file )

    41. (with M. Lehn) Stable pairs on curves and surfaces. J. Alg. Geom. 4 (1995), 67-104. alg-geom/921100

    42. Complete Curves in moduli spaces of stable bundles on surfaces. Math. Ann. 298 (1994), 67-78.