Publications and Preprints:

1. (with M. Nieper-Wisskirchen) Remarks on derived equivalences of Ricci-flat manifolds. in preparation. 23 pages.
   
2. (with E. Macri, P. Stellari) Derived equivalences of K3 surfaces and orientation. 70 pages. arXiv:0710.1645.
   
3. (with E. Macri, P. Stellari) Stability conditions for generic K3 categories. 32 pages. Comp. math. to appear math.AG/0608430.
   
4. Derived and abelian equivalence of K3 surface. Preprint (2006), 26 pages. J. Alg. Geom. to appear math.AG/0604150
   
5. The global Torelli theorem: classical, derived, twisted. submitted to the Proc. of the Seattle conference. Preprint (2006). 23 pages.
   
6. (with R. Thomas) P-objects and autoequivalences of derived categories. MRL 13 (2006), 87-98 math.AG/0507040
7. (with P. Stellari) Proof of Caldararu's conjecture. Adv. Stud. Pure Math. 45. 'Moduli spaces and arithmetic of algebraic varieties.' (2007) math.AG/0411541
8. (with P. Stellari) Equivalences of twisted K3 surfaces. Math. Ann. 332 (2005), 901-936. math.AG/0409030
9. Generalized Calabi-Yau structures, K3 surfaces, and B-fields. Int. J. Math. 16 (2005), 13-36. math.AG/0306162
10. (with S. Schroeer) The Brauer group of analytic K3 surfaces. IMRN. 50 (2003), 2687-2698. math.AG/0305101
11. Moduli spaces of hyperkähler manifolds and mirror symmetry. In: Intersection Theory and Moduli. Proc. Trieste 2002. math.AG/0210219
12.  Finitenes results for hyperkähler manifolds. J. reine angew. Math. 558 (2003), 15-22. math.AG/0109024
13. The Kähler cone of a compact hyperkähler manifold. completely revised version of the 1999 preprint.Math. Ann. 326 (2003), 499-513. math.AG/9909109
14. Erratum to the paper: Compact hyperkähler manifolds: basic results. Invent. math. 152 (2003), 209-212. math.AG/0106014
15. Product of harmonic forms and rational curves. Documenta Mathematica 6 (2001), 227-239.
16. Compact hyperkähler manifolds: Basic results. Invent. Math. 135 (1999), 63 - 113.
17. Compact hyperkähler manifolds. Habilitationsschrift Essen (1997), 65 pages ( ps-file )
18. Birational symplectic manifolds and their deformations. J. Diff. Geom. 45 (1997), 488 - 513. alg-geom/9601015
19. (with L. Göttsche) - Hodge numbers of moduli spaces of stable sheaves on K3 surfaces. Int. J. Math. 7 (1996), 359 -372. alg-geom/9408001
20. The tangent bundle of a Calabi-Yau manifold - Deformations and restrictions to rational curves. Comm. Math. Phys. 171 (1995), 139 - 158. ( ps-file )
21. (with M. Lehn) Framed modules and their moduli. Int. J. Math. 6 (1995), 297 - 324. ( ps-file )
22. (with M. Lehn) Stable pairs on curves and surfaces. J. Alg. Geom. 4 (1995), 67 - 104. alg-geom/921100
    
23. Complete Curves in moduli spaces of stable bundles on surfaces. Math. Ann. 298 (1994), 67 - 78.

1. Fourier-Mukai transforms in Algebraic Geometry. Oxford Mathematical Monographs. 2006. 307 pages.
2. Complex geometry - an introduction. Springer (2004). Universitext. 309 pages.
3. (with D. Joyce, M. Gross) Calabi-Yau manifolds and related geometries. Springer (2002), 244 pages.
4. (with M. Lehn) The geometry of moduli spaces of shaves. Aspects of Mathematics E 31, Vieweg (1997), 260 pages. Unfortunately, we do not find the time to update the book and correct the mistakes known to us. So here is the ps-file of the original version.

1. Projectivity of Kähler manifolds - Kodaira's problem (after C. Voisin) math.AG/0512039
   
2. Moduli of tori and the Narain moduli space. Notes of my talk in the lecture series with M. Lehn and M. Rosellen on "Moduli spaces of toroidal conformal field theories and T-duality". Workshop "Algebraic Aspects of Mirror Symmetry" . Kaiserslautern June 2001 ( ps-file )
3. Geometries on K3 surfaces and their symmetries. Notes of a Colloquium talk given in Berlin and Kyoto. (ps-file )
   

1. Infinitesimal variation of harmonic forms and Lefschetz decomposition. Preprint 2001. 15 pages. math.AG /0102116
2. The Kähler cone of a compact hyperkähler manifold. Preprint 1999. 24 pages (version September.1999 ).