Publications and Preprints


    1. Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci. 21 pages. arXiv:2012.04608
    2. Geometry of K3 surfaces and hyperkaehler manifolds. Plenary talk at the DMV annual meeting 2020. 18 pages pdf

    3. Complex multiplication in twistor spaces. 22 pages. to appear in IMRN. arXiv:1910.13788

    4. (with Chenyang Xu) Lagrangian fibrations of hyperkaehler fourfolds. 12 pages to appear in Journal IJM arXiv:1902.10440

    5. Hodge theory of cubic fourfolds, their Fano varieties, and associated K3 categories. in Lecture Notes of the Unione Matematica Italiana 26, Springer, (2019), 165-198. arXiv:1811.02876

    6. Finiteness of polarized K3 surfaces and hyperkaehler manifolds. 19 pages. Annales Henri Lebesgue 1 (2018) 227--246. arXiv:1801.07040

    7. Motives of isogenous K3 surfaces. 12 pages. Commentarii Mathematici Helvetici 94 (2019), 445-458. arXiv:1705.04063

    8. Motives of derived equivalent K3 surfaces. Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg 88 (2018), 201-207. arXiv:1702.03178

    9. (with J. Rennemo) Hochschild cohomology versus the Jacobian ring, and the Torelli theorem for cubic fourfolds. Algebraic Geometry 6(1) (2019), 76-99 arXiv:1610.04128

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

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

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

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

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

    15. 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

    16. 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

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

    18. 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

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

    20. 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

    21. (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

    22. (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

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

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

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

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

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

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

    29. 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.

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

    31. 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

    32. (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

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

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

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

    36. 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

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

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

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

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

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

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

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

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

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

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

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

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