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Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar)
December 13, 2016 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)

The $4n^2$-inequality for complete intersection singularities

A. V. Pukhlikov

Abstract: The famous $4n^2$-inequality is extended to generic complete intersection singularities: we show that the multiplicity of the self-intersection of a mobile linear system $\Sigma$ with a maximal singularity (i.e. the pair $(X,frac{1}{n}\Sigma)$ is not canonical, where $X$ is the ambient variety) is greater than $4n^2\mu$, where $\mu$ is the multiplicity of the singular point. This inequality essentially simplifies proving birational rigidity for many types of singular Fano varieties.