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3 results

  • Enough vector bundles on orbispaces

  • Part of
  • John Pardon
  • Journal:
    Compositio Mathematica / Volume 158 / Issue 11 / November 2022
    Published online by Cambridge University Press:
    28 November 2022, pp. 2046-2081
    Print publication:
    November 2022
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  • We show that every orbispace satisfying certain mild hypotheses has ‘enough’ vector bundles. It follows that the $K$-theory of finite rank vector bundles on such orbispaces is a cohomology theory. Global presentation results for smooth orbifolds and derived smooth orbifolds also follow.

  • Twisted jets, motivic measures and orbifold cohomology

  • Takehiko Yasuda
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 2 / March 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 396-422
    Print publication:
    March 2004
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  • 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.