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

Abstract

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-Ampère 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.

arXiv comment16 pages

References in corpus (2)

• Differential-geometric methods for the lifting problem and linear systems on plane curves
• On first order Congruences of Lines in ${\mathbb{P}}^4$ with irreducible fundamental Surface

Cited by in corpus (1)

• Systems of conservation laws with third-order Hamiltonian structures