Simple obstructions and cone reduction
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Feng Qu
Abstract
Let X be a Deligne–Mumford stack locally of finite type over an algebraically closed field k of characteristic zero. We show that the intrinsic normal cone CX of X is supported in the subcone 𝕍(ΩX[−1]) of its intrinsic normal sheaf NX. This leads to an alternative proof of cone reduction by cosections for CX. We also discuss vanishing of simple obstructions under the Buchweitz–Flenner semiregularity map for sheaves.
Communicated by: I. Coskun
Acknowledgements
We would like to thank the referee for careful reading and suggestions.
References
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Articles in the same Issue
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals