Euler characteristics of algebraic varieties

Sylvain Cappell, Laurentiu G. Maxim, Julius L. Shaneson

Research output: Contribution to journalArticle

Abstract

This note studies the behavior of Euler characteristics and of intersection homology Euler characteristics under proper morphisms of algebraic (respectively, analytic) varieties. The methods also yield, for algebraic (respectively, analytic) varieties, formulae comparing these two kinds of Euler characteristics. The main results are direct consequences of the calculus of constructible functions and Grothendieck groups of constructible sheaves. Similar formulae for Hodge-theoretic invariants of algebraic varieties under morphisms were announced by the first and third authors in [5,14].

Original languageEnglish (US)
Pages (from-to)409-421
Number of pages13
JournalCommunications on Pure and Applied Mathematics
Volume61
Issue number3
DOIs
StatePublished - Mar 2008

Fingerprint

Algebraic Variety
Euler Characteristic
Constructible
Morphisms
Intersection Homology
Grothendieck Group
Sheaves
Calculus
Invariant

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Euler characteristics of algebraic varieties. / Cappell, Sylvain; Maxim, Laurentiu G.; Shaneson, Julius L.

In: Communications on Pure and Applied Mathematics, Vol. 61, No. 3, 03.2008, p. 409-421.

Research output: Contribution to journalArticle

Cappell, Sylvain ; Maxim, Laurentiu G. ; Shaneson, Julius L. / Euler characteristics of algebraic varieties. In: Communications on Pure and Applied Mathematics. 2008 ; Vol. 61, No. 3. pp. 409-421.
@article{8a16ce458b2946c9869dbc854e921ff4,
title = "Euler characteristics of algebraic varieties",
abstract = "This note studies the behavior of Euler characteristics and of intersection homology Euler characteristics under proper morphisms of algebraic (respectively, analytic) varieties. The methods also yield, for algebraic (respectively, analytic) varieties, formulae comparing these two kinds of Euler characteristics. The main results are direct consequences of the calculus of constructible functions and Grothendieck groups of constructible sheaves. Similar formulae for Hodge-theoretic invariants of algebraic varieties under morphisms were announced by the first and third authors in [5,14].",
author = "Sylvain Cappell and Maxim, {Laurentiu G.} and Shaneson, {Julius L.}",
year = "2008",
month = "3",
doi = "10.1002/cpa.20201",
language = "English (US)",
volume = "61",
pages = "409--421",
journal = "Communications on Pure and Applied Mathematics",
issn = "0010-3640",
publisher = "Wiley-Liss Inc.",
number = "3",

}

TY - JOUR

T1 - Euler characteristics of algebraic varieties

AU - Cappell, Sylvain

AU - Maxim, Laurentiu G.

AU - Shaneson, Julius L.

PY - 2008/3

Y1 - 2008/3

N2 - This note studies the behavior of Euler characteristics and of intersection homology Euler characteristics under proper morphisms of algebraic (respectively, analytic) varieties. The methods also yield, for algebraic (respectively, analytic) varieties, formulae comparing these two kinds of Euler characteristics. The main results are direct consequences of the calculus of constructible functions and Grothendieck groups of constructible sheaves. Similar formulae for Hodge-theoretic invariants of algebraic varieties under morphisms were announced by the first and third authors in [5,14].

AB - This note studies the behavior of Euler characteristics and of intersection homology Euler characteristics under proper morphisms of algebraic (respectively, analytic) varieties. The methods also yield, for algebraic (respectively, analytic) varieties, formulae comparing these two kinds of Euler characteristics. The main results are direct consequences of the calculus of constructible functions and Grothendieck groups of constructible sheaves. Similar formulae for Hodge-theoretic invariants of algebraic varieties under morphisms were announced by the first and third authors in [5,14].

UR - http://www.scopus.com/inward/record.url?scp=38949173870&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38949173870&partnerID=8YFLogxK

U2 - 10.1002/cpa.20201

DO - 10.1002/cpa.20201

M3 - Article

VL - 61

SP - 409

EP - 421

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 3

ER -