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SUMMARY:Anthony Varilly-Alvarado (Rice University)
DTSTART:20210527T150000Z
DTEND:20210527T160000Z
DTSTAMP:20260423T021344Z
UID:ZAG/124
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/124/">Qu
 asi-hyperbolicity via explicit symmetric differentials</a>\nby Anthony Var
 illy-Alvarado (Rice University) as part of ZAG (Zoom Algebraic Geometry) s
 eminar\n\n\nAbstract\nA surface X is algebraically quasi-hyperbolic if it 
 contains finitely many curves of genus 0 or 1.  In 2006\, Bogomolov and de
  Oliveira used asymptotic computations to show that sufficiently nodal sur
 faces of high degree in projective three-space carry symmetric differentia
 ls\, and they used this to prove quasi-hyperbolicity of these surfaces.  W
 e explain how a granular analysis of their ideas\, combined with computati
 onal tools and insights\, yield explicit results for the existence of symm
 etric differentials\, and we show how these results can be used to give co
 nstraints on the locus of rational curves on surfaces like the Barth Decic
 \, Buechi's surface\, and certain complete intersections of general type\,
  including the surface parametrizing perfect cuboids\, and the surface par
 ametrizing magic squares of squares.  This is joint work with Nils Bruin a
 nd Jordan Thomas.\n
LOCATION:https://researchseminars.org/talk/ZAG/124/
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