Congruences of lines in $\mathbb{P}^5$, quadratic normality, and completely exceptional Monge-Ampère equations

Details Congruences of lines in $\mathbb{P}^5$, quadratic normality, and completely exceptional Monge-Ampère equations Congruences of lines in $\mathbb{P}^5$, quadratic normality, and completely exceptional Monge-Ampère equations

2007-10-26

arxiv.org/abs/0710.5110v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

The existence is proved of two new families of locally Cohen-Macaulay sextic threefolds in $\mathbb{P}^5$, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge-Amp\`ere equations. One of these families comes from a smooth congruence of multidegree $(1,3,3)$ which is a smooth Fano fourfold of index two and genus 9.

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