Holomorphic Morse Inequalities

  title={Holomorphic Morse Inequalities},
  author={Jean-Pierre DEMAILLY},
  • Jean-Pierre DEMAILLY
  • Published 1991
Let M be a compact C manifold, dimR M = m, and h a Morse function, i.e. a function such that all critical points are non degenerate. The standard Morse inequalities relate the Betti numbers bq = dimH q DR(M,R) and the numbers sq = # critical points of index q , where the index of a critical point is the number of negative eigenvalues of the Hessian form (∂h/∂xi∂xj). Specifically, the following “strong Morse inequalities” hold : 
Highly Cited
This paper has 23 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
18 Citations
7 References
Similar Papers


Publications referenced by this paper.
Showing 1-7 of 7 references

Some recent results in complex manifold theory related to vanishing theorems for the semi-positive case

  • Siu y.t
  • Proceedings of the Math. Arbeitstagung
  • 1984

A vanishing theorem for semipositive line bundles over nonKähler manifolds

  • Siu y
  • J . Differential Geometry

Champs magnétiques et inégalités de Morse pour la d ′ ′cohomologie

  • Demailly j, Sém. P. Lelong, P. Dolbeault
  • Ann . Inst . Fourier

Metric on invertible sheaves on abelian varieties , preprint  , Johns Hopkins Univ

  • Siu y
  • Akad . Wiss . Göttingen Math . Phys . K .

On the heat equation and the index theorem

  • Atiyah m. f.
  • Invent . Math .

The index of elliptic operators III Demailly ’ s asymptotic inequalities : a heat equation proof

  • Singer i. m.
  • J . Funct . Analysis

Théorèmes de finitude pour la cohomologie des espaces complexes

  • Grauert h.
  • Bull . Soc . Math . France

Similar Papers

Loading similar papers…