Holomorphic Morse inequalities on manifolds with boundary

• Let X be a compact complex manifold with boundary and let L-k be a high power of a hermitian holomorphic line bundle over X. When X has no boundary, Demailly's holomorphic Morse inequalities give asymptotic bounds on the dimensions of the Dolbeault cohomology groups with values in Lk, in terms of the curvature of L. We extend Demailly's inequalities to the case when X has a boundary by adding a boundary term expressed as a certain average of the curvature of the line bundle and the Levi curvature of the boundary. Examples are given that show that the inequalities are sharp.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Algebra, geometri och analys

Algebra, geometry and mathematical analysis

line bundles

cohomology

harmonic forms

holomorphic sections

Bergman

kernel

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)