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SUMMARY:Tony Yue Yu (Université Paris-Sud\, Paris-Saclay)
DTSTART:20201009T153000Z
DTEND:20201009T170000Z
DTSTAMP:20260423T041526Z
UID:UBC-AG/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UBC-AG/3/">S
 econdary fan\, theta functions and moduli of Calabi-Yau pairs</a>\nby Tony
  Yue Yu (Université Paris-Sud\, Paris-Saclay) as part of UBC Vancouver Al
 gebraic Geometry Seminar\n\n\nAbstract\nWe conjecture that any connected c
 omponent Q of the moduli space of triples (X\,E=E1+⋯+En\,Θ) where X is 
 a smooth projective variety\, E is a normal crossing anti-canonical diviso
 r with a 0-stratum\, every Ei is smooth\, and Θ is an ample divisor not c
 ontaining any 0-stratum of E\, is \\emph{unirational}. More precisely: not
 e that Q has a natural embedding into the Kollár-Shepherd-Barron-Alexeev 
 moduli space of stable pairs\, we conjecture that its closure admits a fin
 ite cover by a complete toric variety. We construct the associated complet
 e toric fan\, generalizing the Gelfand-Kapranov-Zelevinski secondary fan f
 or reflexive polytopes. Inspired by mirror symmetry\, we speculate a synth
 etic construction of the universal family over this toric variety\, as the
  Proj of a sheaf of graded algebras with a canonical basis\, whose structu
 re constants are given by counts of non-archimedean analytic disks. In the
  Fano case and under the assumption that the mirror contains a Zariski ope
 n torus\, we construct the conjectural universal family\, generalizing the
  families of Kapranov-Sturmfels-Zelevinski and Alexeev in the toric case. 
 In the case of del Pezzo surfaces with an anti-canonical cycle of (−1)-c
 urves\, we prove the full conjecture. The reference is arXiv:2008.02299 jo
 int with Hacking and Keel.\n
LOCATION:https://researchseminars.org/talk/UBC-AG/3/
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