Journal of Algebraic Geometry

Author(s): Marc A. Nieper
Journal: J. Algebraic Geom. 12 (2003), 715-739.
Posted: June 26, 2003
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Abstract: In this article we investigate Hirzebruch-Riemann-Roch formulae for line bundles on irreducible symplectic Kähler manifolds. As Huybrechts has shown, for every irreducible symplectic Kähler manifold

of dimension

, there are numbers $a_0, a_2, \dots, a_{2n}$ such that

Using Rozansky-Witten classes similarly to Hitchin and Sawon, we obtain a closed formula expressing the $a_{2k}$ in terms of Chern numbers of

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Marc A. Nieper
Affiliation: Mathematisches Institut der Univ. zu Köln, Weyertal 86--90, 50931 Köln, Germany
Address at time of publication: Schillingstr. 1, 50670 Köln. Germany
Email: mail@marc-nieper.de, marc@nieper-wisskirchen.de

PII: S 1056-3911(03)00325-4
Received by editor(s): April 10, 2001
Received by editor(s) in revised form: August 22, 2001
Posted: June 26, 2003
Additional Notes: We are very grateful to Daniel Huybrechts for having carefully read preliminary versions of this paper, and to Michael Britze, Daniel Huybrechts, Manfred Lehn and many others for their support to us and helpful discussions about the subject

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