Abstract
We show that there exist smooth surfaces violating Generic Vanishing in any characteristic \(p \ge 3\). As a corollary, we recover a result of Hacon and Kovács, producing counterexamples to Generic Vanishing in dimension 3 and higher.
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Notes
In the following, we will consider
with L ample. In this case, we will have \(i(M)=\dim B\), and \(|\chi (M)|=h^0(L)\).
with L ample. In this case, we will have References
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Acknowledgements
The author would like to thank his advisor Christopher Hacon for suggesting the problem, for his insightful suggestions and the encouragement. He would also like to thank Karl Schwede for the helpful conversations, and Andrew Bydlon for the many times he listened to his doubts and ideas. Finally, he would like to thank Hanna Astephan for the continuous feedback about his writing.
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The author was partially supported by DMS-1300750, DMS-1265285 and a grant from the Simons Foundation, Award Number 256202.
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Filipazzi, S. Generic vanishing fails for surfaces in positive characteristic. Boll Unione Mat Ital 11, 179–189 (2018). https://doi.org/10.1007/s40574-017-0120-6
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DOI: https://doi.org/10.1007/s40574-017-0120-6