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UID:c3967bfc833bf4c2c840446155afb8cf
CATEGORIES:Colloquia
CREATED:20251017T132051
SUMMARY:Compactifying Moduli of Algebraic Varieties
LOCATION:Hill 705
DESCRIPTION:Hodge Theory provides a general way of understanding moduli spaces of algeb
 raic varieties: Given a family of algebraic varieties, one obtains a `perio
 d map' by considering the hodge structure on the cohomology. However, these
  period maps are built from period integrals, and are highly transcendental
 , which yields challenges when one wants to recover an algebraic structure.
  \nFamously, this story works really nicely for the moduli space of (princi
 pally polarized, g-dimensional) Abelian varieties A_g, where the hodge theo
 ry gives an exact moduli space, and the work of Baily-Borel provides a beau
 tiful compactification of this space which can also be understood using hod
 ge theory. \nWe explain how this picture generalizes to arbitrary period ma
 ps. This has especially nice applications to moduli spaces of Calabi-Yaus, 
 which has proven less accessible to other techniques. Moreover, the same to
 ols yield a resolution of the  b-semiampleness conjecture of Prokhorov and 
 Shokurov. This is joint work with Bakker, Filipazzi, and Mauri.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Hodge Theory provides a general way of understanding moduli spaces of al
 gebraic varieties: Given a family of algebraic varieties, one obtains a `pe
 riod map' by considering the hodge structure on the cohomology. However, th
 ese period maps are built from period integrals, and are highly transcenden
 tal, which&nbsp;yields challenges when one wants to recover an algebraic st
 ructure.&nbsp;</p><p>Famously, this story works really nicely for the modul
 i space of (principally polarized, g-dimensional) Abelian varieties A_g, wh
 ere the hodge theory gives an exact&nbsp;moduli space, and the work of Bail
 y-Borel provides a beautiful compactification of this space which can also 
 be understood using hodge theory.&nbsp;</p><p>We explain how this picture g
 eneralizes to arbitrary period maps. This has especially nice applications 
 to moduli spaces of Calabi-Yaus, which has proven less accessible to other&
 nbsp;techniques. Moreover, the same tools yield a resolution of the&nbsp; b
 -semiampleness conjecture of Prokhorov and Shokurov. This is joint work wit
 h Bakker, Filipazzi, and Mauri.</p>
CONTACT:Jacob Tsimerman
DTSTAMP:20260827T115847
DTSTART;TZID=America/New_York:20251024T153000
DTEND;TZID=America/New_York:20251024T163000
SEQUENCE:0
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