September 2019 Anti-pluricanonical systems on Fano varieties
Caucher Birkar
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Ann. of Math. (2) 190(2): 345-463 (September 2019). DOI: 10.4007/annals.2019.190.2.1

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. "Anti-pluricanonical systems on Fano varieties." Ann. of Math. (2) 190 (2) 345 - 463, September 2019. https://doi.org/10.4007/annals.2019.190.2.1

Information

Published: September 2019
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2019.190.2.1

Subjects:
Primary: 14C20 , 14E05 , 14E30 , 14J45

Keywords: complements , Fano varieties , Linear systems , minimal model program

Rights: Copyright © 2019 Department of Mathematics, Princeton University

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Vol.190 • No. 2 • September 2019
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