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arXiv · 1603.05765

Anti-pluricanonical systems on Fano varieties

Caucher Birkar
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Abstract

In this paper, we study the linear systems $|-mK_X|$ on Fano varieties $X$ with klt singularities. In a given dimension $d$, we prove $|-mK_X|$ is non-empty and contains an element with "good singularities" for some natural number $m$ depending only on $d$; if in addition $X$ is $\epsilon$-lc for some $\epsilon>0$, then we show that we can choose $m$ depending only on $d$ and $\epsilon$ so that $|-mK_X|$ defines a birational map. Further, we prove Shokurov's conjecture on boundedness of complements, and show that certain classes of Fano varieties form bounded families.

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Caucher Birkar. 2016-03-18. Anti-pluricanonical systems on Fano varieties. https://arxiv.org/abs/1603.05765

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