Publications and Preprints


    1. The K3 category of a cubic fourfold - an update. 15 pages. not submitted pdf

    2. Chow groups of surfaces of lines in cubic fourfolds. 15 pages. arXiv:2211.12186 to appear in EpiGA

    3. (with O. Debarre, E. Macri, C. Voisin) Computing Riemann--Roch polynomials and classifying hyper-Kaehler fourfolds 34 pages. arXiv:2201.08152 to appear in JAMS

    4. (with T. Beckmann) Dual fibrations. 19 pages. not submitted pdf

    5. (with F. Anella) Characteristic foliations 19 pages. submitted arXiv:2201.07624

    6. (with an appendix by J. Ottem) Nodal quintic surfaces and lines on cubic fourfolds. 27 pages. to appear in L'Enseignement mathematique arXiv:2108.10532

    7. (with M. Mauri) On type II degenerations of hyperkaehler manifolds. 12 pages. to appear in MRL arXiv:2108.01587

    8. (with M. Mauri) Lagrangian fibrations. 24 pages. arXiv:2108.10193 Milan Journal Math. 90 (2022), 459-483.

    9. (with F. Anella) Effectivity of semipositive line bundles 13 pages. pdf Milan Journal Math. 9 (2022), 389-401

    10. (with Y. Dutta) Maximal variation of curves on K3 surfaces. 19 pages. Tunisian J. Math. 4 (2022), 443-464 arXiv:2105.04787

    11. Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci. 21 pages. to appear in Annals de la Faculte des Sciences de Toulouse arXiv:2012.04608

    12. Geometry of K3 surfaces and hyperkaehler manifolds. Plenary talk at the DMV annual meeting 2020. 18 pages. not submitted pdf

    13. Complex multiplication in twistor spaces. 22 pages. IMRN 2022, 3 (2022), 2095-2122. arXiv:1910.13788

    14. (with Chenyang Xu) Lagrangian fibrations of hyperkaehler fourfolds. Journal IJM 21 (2022), 921-932 arXiv:1902.10440

    15. 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

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

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

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

    19. (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

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

    21. On derived categories of K3 surfaces, symplectic automorphisms, and the Conway group. 16 pages. Advanced Studies in Pure Math. 69 (Math. Soc. Japan) 2016 arXiv:1309.6528

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

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

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

    25. 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. videos 47 pages. arXiv:1111.1745v1

    26. 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

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

    28. 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

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

    30. 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

    31. (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

    32. (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

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

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

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

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

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

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

    39. 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.

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

    41. 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

    42. (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

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

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

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

    46. 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

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

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

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

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

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

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

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

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

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

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

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

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