Hassett, Brendan EVarilly-Alvarado, Anthony2017-07-312017-07-312016-122016-11-01December 2Allums, Derek. "Notes on Real Rationally Connected Varieties and Fano Threefolds of Genus 12." (2016) Diss., Rice University. <a href="https://hdl.handle.net/1911/95585">https://hdl.handle.net/1911/95585</a>.https://hdl.handle.net/1911/95585We 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 a smooth projective curve. Additionally, we show that many real smooth Fano complete intersections admit non-constant maps 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.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.rationally connected varietiesfano threefoldsV22torelli theoremreal varietiesThesis2017-07-31