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# Singularities of anticanonical divisors

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Liana Heuberger (Nice)

What SFB-Kolloquium Jan 07, 2016 from 03:30 pm to 04:30 pm Mainz, 05-432 (Hilbertraum) vCal iCal

Let $X$ be a Fano variety. A result by Shokurov states that in dimension three the linear system $|-K_X|$ is non empty and a general element $D$ in $|-K_X|$ is smooth. In dimension four, one can construct Fano varieties $X$ so that every such $D$ is singular, however we show it has at most terminal singularities. We also determine explicit local equations of $D$ around these points.