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arXiv · 1407.7632

A vanishing theorem on fake projective planes with enough automorphisms

JongHae Keum
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Abstract

For every fake projective plane $X$ with automorphism group of order 21, we prove that $H^i(X, 2L)=0$ for all $i$ and for every ample line bundle $L$ with $L^2=1$. For every fake projective plane with automorphism group of order 9, we prove the same vanishing for every cubic root (and its twist by a 2-torsion) of the canonical bundle $K$. As an immediate consequence, there are exceptional sequences of length 3 on such fake projective planes.

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JongHae Keum. 2015-02-05. A vanishing theorem on fake projective planes with enough automorphisms. https://arxiv.org/abs/1407.7632

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