Hodge numbers attached to a polynomial map

R. García López; A. Némethi

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 5, page 1547-1579
  • ISSN: 0373-0956

Abstract

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We attach a limit mixed Hodge structure to any polynomial map f : n . The equivariant Hodge numbers of this mixed Hodge structure are invariants of f which reflect its asymptotic behaviour. We compute them for a generic class of polynomials in terms of equivariant Hodge numbers attached to isolated hypersurface singularities and equivariant Hodge numbers of cyclic coverings of projective space branched along a hypersurface. We show how these invariants allow to determine topological invariants of f such as the real Seifert form at infinity.

How to cite

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López, R. García, and Némethi, A.. "Hodge numbers attached to a polynomial map." Annales de l'institut Fourier 49.5 (1999): 1547-1579. <http://eudml.org/doc/75393>.

@article{López1999,
abstract = {We attach a limit mixed Hodge structure to any polynomial map $f:\{\Bbb C\}^n\rightarrow \{\Bbb C\}$. The equivariant Hodge numbers of this mixed Hodge structure are invariants of $f$ which reflect its asymptotic behaviour. We compute them for a generic class of polynomials in terms of equivariant Hodge numbers attached to isolated hypersurface singularities and equivariant Hodge numbers of cyclic coverings of projective space branched along a hypersurface. We show how these invariants allow to determine topological invariants of $f$ such as the real Seifert form at infinity.},
author = {López, R. García, Némethi, A.},
journal = {Annales de l'institut Fourier},
keywords = {mixed Hodge structures; polynomial maps; hypersurface singularities},
language = {eng},
number = {5},
pages = {1547-1579},
publisher = {Association des Annales de l'Institut Fourier},
title = {Hodge numbers attached to a polynomial map},
url = {http://eudml.org/doc/75393},
volume = {49},
year = {1999},
}

TY - JOUR
AU - López, R. García
AU - Némethi, A.
TI - Hodge numbers attached to a polynomial map
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 5
SP - 1547
EP - 1579
AB - We attach a limit mixed Hodge structure to any polynomial map $f:{\Bbb C}^n\rightarrow {\Bbb C}$. The equivariant Hodge numbers of this mixed Hodge structure are invariants of $f$ which reflect its asymptotic behaviour. We compute them for a generic class of polynomials in terms of equivariant Hodge numbers attached to isolated hypersurface singularities and equivariant Hodge numbers of cyclic coverings of projective space branched along a hypersurface. We show how these invariants allow to determine topological invariants of $f$ such as the real Seifert form at infinity.
LA - eng
KW - mixed Hodge structures; polynomial maps; hypersurface singularities
UR - http://eudml.org/doc/75393
ER -

References

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