

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^{} 
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Abstract:
The famous $4n^2$inequality is extended to generic
complete intersection singularities: we show that the multiplicity
of the selfintersection 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.

