Publications and Preprints


    1. (with D. Mattei) The special Brauer group and twisted Picard varieties. 26 pages. arXiv:2310.04032

    2. (with D. Mattei) Splitting unramified Brauer classes by abelian torsors and the period-index problem. 19 pages. arXiv:2310.04029

    3. The K3 category of a cubic fourfold - an update. 15 pages. arXiv:2303.03820

    4. Chow groups of surfaces of lines in cubic fourfolds. 15 pages. arXiv:2211.12186 EpiGA (2023) Art 5

    5. (with O. Debarre, E. Macri, C. Voisin) Computing Riemann--Roch polynomials and classifying hyper-Kaehler fourfolds. JAMS 37, (2024), 151-185. arXiv:2201.08152

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

    7. (with F. Anella) Characteristic foliations. to appear in Bull. LMS arXiv:2201.07624

    8. (with an appendix by J. Ottem) Nodal quintic surfaces and lines on cubic fourfolds. 27 pages. L'Enseignement mathematique 70 (2024), 499-532. arXiv:2108.10532

    9. (with M. Mauri) On type II degenerations of hyperkaehler manifolds. Math. Res. Lett. 30 (2023), no. 1, 125-141 arXiv:2108.01587

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

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

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

    13. Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci. Ann. Fac. Sci. Toulouse Math. (6) 32 (2023), no. 2, 397-421 arXiv:2012.04608

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

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

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

    17. 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

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

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

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

    21. (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

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

    23. 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

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

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

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

    27. 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

    28. 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

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

    30. 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

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

    32. 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

    33. (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

    34. (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

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

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

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

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

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

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

    41. 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.

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

    43. 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

    44. (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

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

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

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

    48. 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

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

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

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

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

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

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

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

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

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

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

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

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