Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-20T18:31:00.146Z Has data issue: false hasContentIssue false
  • English
  • Français

Twisted jets, motivic measures and orbifold cohomology

Published online by Cambridge University Press:  04 December 2007

Takehiko Yasuda
Takehiko Yasuda
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153-8914, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We introduce the notion of twisted jets. For a Deligne–Mumford stack $\mathscr{X}$ of finite type over $\mathbb{C}$, a twisted $\infty$-jet on $\mathscr{X}$ is a representable morphism $\mathscr{D} \to \mathscr{X}$ such that $\mathscr{D}$ is a smooth Deligne–Mumford stack with the coarse moduli space Spec$\mathbb{C}[[t]]$. We study a motivic measure on the space of the twisted $\infty$-jets on a smooth Deligne–Mumford stack. As an application, we prove that two birational minimal models with Gorenstein quotient singularities have the same orbifold cohomology as a Hodge structure.

Keywords

twisted jetsDeligne–Mumford stacksmotivic measureorbifold cohomologyGorenstein quotient singularities14F43 (primary)14B0514B1014E15 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 2 , March 2004 , pp. 396 - 422
Copyright
Foundation Compositio Mathematica 2004