Primitive cohomology and the tube mapping

Christian Schnell

doi:10.1007/s00209-010-0710-9

Primitive cohomology and the tube mapping

Christian Schnell

Mathematics

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

Abstract

Let X be a smooth complex projective variety of dimension d. We show that its primitive cohomology in degree d is generated by certain "tube classes," constructed from the monodromy in the family of all hyperplane sections of X. The proof makes use of a result about the group cohomology of certain representations that may be of independent interest.

Original language	English
Pages (from-to)	1069-1089
Number of pages	21
Journal	Mathematische Zeitschrift
Volume	268
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-010-0710-9
State	Published - Aug 2011

Keywords

Group cohomology
Lefschetz pencil
Monodromy
Primitive cohomology

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10.1007/s00209-010-0710-9

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abstract = "Let X be a smooth complex projective variety of dimension d. We show that its primitive cohomology in degree d is generated by certain {"}tube classes,{"} constructed from the monodromy in the family of all hyperplane sections of X. The proof makes use of a result about the group cohomology of certain representations that may be of independent interest.",

keywords = "Group cohomology, Lefschetz pencil, Monodromy, Primitive cohomology",

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T1 - Primitive cohomology and the tube mapping

AU - Schnell, Christian

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N2 - Let X be a smooth complex projective variety of dimension d. We show that its primitive cohomology in degree d is generated by certain "tube classes," constructed from the monodromy in the family of all hyperplane sections of X. The proof makes use of a result about the group cohomology of certain representations that may be of independent interest.

AB - Let X be a smooth complex projective variety of dimension d. We show that its primitive cohomology in degree d is generated by certain "tube classes," constructed from the monodromy in the family of all hyperplane sections of X. The proof makes use of a result about the group cohomology of certain representations that may be of independent interest.

KW - Group cohomology

KW - Lefschetz pencil

KW - Monodromy

KW - Primitive cohomology

UR - https://www.scopus.com/pages/publications/79960149422

U2 - 10.1007/s00209-010-0710-9

DO - 10.1007/s00209-010-0710-9

M3 - Article

AN - SCOPUS:79960149422

SN - 0025-5874

VL - 268

SP - 1069

EP - 1089

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Primitive cohomology and the tube mapping

Abstract

Keywords

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