Twisted jets, motivic measure and orbifold cohomology

Abstract

We introduce the notion of twisted jet on a Deligne-Mumford stack. and study the 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 with Hodge structure.

34 pages, to appear in Compositio Mathematica

References in corpus (2)

• A New Cohomology Theory for Orbifold
• Stringy Geometry and Topology of Orbifolds

Cited by in corpus (41)

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• Francia's flip and derived categories
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• Cohomology ring of crepant resolutions of orbifolds
• On semi-continuity problems for minimal log discrepancies
• Toward motivic integration over wild Deligne-Mumford stacks
• Wilder McKay correspondences
• On genus one mirror symmetry in higher dimensions and the BCOV conjectures
• Stringy invariants for horospherical varieties of complexity one
• The Orbifold Chow Ring of Hypertoric Deligne-Mumford Stacks
• Birational Calabi-Yau 3-folds and BPS state counting
• Inversion of adjunction for quotient singularities
• Motivic Integration on the Hitchin Fibration
• Doubling construction of Calabi-Yau threefolds
• Motivic Zeta Functions on $\mathds{Q}$-Gorenstein Varieties
• Motivic integration and the birational invariance of BCOV invariants
• Stringy invariants and toric Artin stacks
• Ehrhart polynomials and stringy Betti numbers
• Motivic integration over wild Deligne-Mumford stacks
• On the stringy Hodge numbers of mirrors of quasi-smooth Calabi-Yau hypersurfaces
• Motivic Integration on Toric Stacks
• On Virasoro Constraints for Orbifold Gromov-Witten Theory
• G2-manifolds from K3 surfaces with non-symplectic automorphisms
• Connecting certain rigid birational non-homeomorphic Calabi--Yau threefolds via Hilbert scheme
• A motivic change of variables formula for Artin stacks
• On the Hard Lefschetz property of stringy Hodge numbers
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• Mckay Correspondence in Quasitoric Orbifolds
• Hodge structures Orbifold hodge numbers and a correspondence in Quasitoric Orbifolds
• Stringy Hodge numbers of strictly canonical nondegenerate singularities
• Borcea-Voisin Calabi-Yau threefolds and invertible potentials
• Motivic multiplicative McKay correspondence for surfaces
• Smooth Calabi-Yau varieties with large index and Betti numbers
• Families of Calabi-Yau hypersurfaces in $\mathbb{Q}$-Fano toric varieties
• A Closer Look ar Mirrors and Quotients of Calabi-Yau Threefolds
• Open problems in the wild McKay correspondence and related fields
• Almost complex structure, blowdowns and McKay correspondence in quasitoric orbifolds
• Quotients of the Dwork Pencil
• Extensions of two Chow stability criteria to positive characteristics
• Arithmetic McKay correspondence