The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
-
Howard Nuer
and
Alan Sorani
Abstract
This note generalizes the celebrated Bogomolov–Gieseker inequality for smooth projective surfaces over an algebraically closed field of characteristic zero to projective surfaces in arbitrary characteristic with canonical singularities. We also generalize to this context some classical applications of the Bogomolov–Gieseker inequality.
Acknowledgements
The seed for the ideas here was planted during conversations at Northeastern University between the first author and Emanuele Macrì. He thanks Emanuele for these productive conversations and Northeastern for providing a conducive research environment. The authors would also like to thank Izzet Coskun and Evgeny Shinder for illuminating discussions during the writing of this paper. They would especially like to thank Adrian Langer for bringing to their attention a problem with the original version of the paper and suggesting how to fix it as well reminding them of the reference [24]. Finally, they would like to thank the referee who made a number of useful comments that improved the exposition.
Communicated by: I. Coskun
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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
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
