Vanishing homology of projective hypersurfaces with 1-dimensional singularities

Dirk Siersma; Mihai Tibăr

doi:10.1007/s40879-017-0151-7

Vanishing homology of projective hypersurfaces with 1-dimensional singularities

Dirk Siersma
, Mihai Tibăr

CNRS

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We introduce and study the vanishing homology of singular projective hypersurfaces. We prove its concentration in two levels in case of 1-dimensional singular locus Σ , and moreover determine the ranks of the nontrivial homology groups. These two groups depend on the monodromy at special points of Σ and on the effect of the monodromy of the local system over its complement.

Original language	English
Pages (from-to)	565-586
Number of pages	22
Journal	Central European Journal of Mathematics
Volume	3
Issue number	3
DOIs	https://doi.org/10.1007/s40879-017-0151-7
Publication status	Published - 1 Sept 2017

Keywords

Monodromy
Nonisolated singularities
Singular projective hypersurfaces
Vanishing homology

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https://arxiv.org/pdf/1411.2640.pdf

Cite this

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title = "Vanishing homology of projective hypersurfaces with 1-dimensional singularities",

abstract = "We introduce and study the vanishing homology of singular projective hypersurfaces. We prove its concentration in two levels in case of 1-dimensional singular locus Σ , and moreover determine the ranks of the nontrivial homology groups. These two groups depend on the monodromy at special points of Σ and on the effect of the monodromy of the local system over its complement.",

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AU - Siersma, Dirk

AU - Tibăr, Mihai

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N2 - We introduce and study the vanishing homology of singular projective hypersurfaces. We prove its concentration in two levels in case of 1-dimensional singular locus Σ , and moreover determine the ranks of the nontrivial homology groups. These two groups depend on the monodromy at special points of Σ and on the effect of the monodromy of the local system over its complement.

AB - We introduce and study the vanishing homology of singular projective hypersurfaces. We prove its concentration in two levels in case of 1-dimensional singular locus Σ , and moreover determine the ranks of the nontrivial homology groups. These two groups depend on the monodromy at special points of Σ and on the effect of the monodromy of the local system over its complement.

KW - Monodromy

KW - Nonisolated singularities

KW - Singular projective hypersurfaces

KW - Vanishing homology

UR - https://www.scopus.com/pages/publications/85028023705

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DO - 10.1007/s40879-017-0151-7

M3 - Article

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SP - 565

EP - 586

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

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ER -

Vanishing homology of projective hypersurfaces with 1-dimensional singularities

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Keywords

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