Rice University Math

2017 Ph.D Thesis Defenses

Derek Allums

Title: Notes on Real Rationally Connected Varieties and Fano Threefolds of Genus 12
Date: Thursday, June 16, 2016
Thesis Advisor: Brendan Hassett

We show that a smooth projective geometrically rationally connected variety over the real numbers with at least one rational point admits a non-constant mapping from an a smooth projective curve. Additionally, we show that a real smooth Fano complete intersection admits a non-constant map from the real anisotropic conic. Furthermore, we compute the genus and degree of the singular locus of the locus of lines on a genus 12 Fano threefold. After blowing up this locus to obtain simple normal crossings divisor, we compute the cohomology of the complement, in which we see the genus of this curve appear in weight 5 of the third cohomology group.