Algebraic intersection spaces

Christian August Geske*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We define a variant of intersection space theory that applies to many compact complex and real analytic spaces X, including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to apply to a particular subclass of spaces with smooth singular sets. We verify existence of these so-called algebraic intersection spaces and show that they are the (reduced) chain complexes of known topological intersection spaces in the case that both exist. We next analyze "local duality obstructions," which we can choose to vanish, and verify that algebraic intersection spaces satisfy duality in the absence of these obstructions. We conclude by defining an untwisted algebraic intersection space pairing, whose signature is equal to the Novikov signature of the complement in X of a tubular neighborhood of the singular set.

Original languageEnglish (US)
Pages (from-to)1-38
Number of pages38
JournalJournal of Topology and Analysis
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Intersection
Singular Set
Obstruction
Duality
Signature
Verify
Projective Variety
Pairing
Vanish
Complement
Choose

Keywords

  • Intersection spaces
  • complex varieties
  • duality
  • intersection homology
  • signature

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

Cite this

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Algebraic intersection spaces. / Geske, Christian August.

In: Journal of Topology and Analysis, 01.01.2019, p. 1-38.

Research output: Contribution to journalArticle

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