Holomorphic Morse inequalities and asymptotic cohomology groups: a tribute to Bernhard Riemann

Jean-Pierre Demailly (1)

1 IF - Institut Fourier

The goal of this note is to present the potential relationships between certain Monge-Ampère integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of line bundles, as recently introduced by algebraic geometers. The expected most general statements are still conjectural and owe a debt to Riemann's pioneering work, which led to the concept of Hilbert polynomials and to the Hirzebruch-Riemann-Roch formula during the XX-th century.

Domaines: Variables complexes [math.CV]

Jean-Pierre Demailly. Holomorphic Morse inequalities and asymptotic cohomology groups: a tribute to Bernhard Riemann. Riemann International School of Mathematics: Advances in Number Theory and Geometry, Apr 2009, Verbania, Italy. 14 p. ⟨hal-00462954⟩