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DTSTART:20070311T020000
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DTSTAMP:20261109T112728
DTSTART;TZID=America/Detroit:20261113T150000
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SUMMARY:Workshop / Seminar:Student Algebraic Geometry: Compactifications of Siegel Modular Varieties
DESCRIPTION:The Siegel upper half-space H_g serves as a natural generalization of the upper half-plane. Indeed\, just as M_{1\,1} = A_1 is the quotient H/SL_2(Z)\, one can show that A_g\, the space of principally polarized abelian varieties of dimension g\, is isomorphic to H_g/Sp_{2g}(Z). More generally\, one can consider spaces H_g/Gamma for any arithmetic subgroup Gamma in Sp_{2g}(Q). Unlike M_g\, which admits the canonical Deligne-Mumford compactification\, these spaces admit many natural compactifications with different geometric properties. In this talk\, we introduce H_g/Gamma\, the Siegel modular varieties\, and discuss various compactifications such as the Baily–Borel compactification and toroidal compactifications. We then focus on the specific case of g = 2 to showcase the beautiful arithmetic that occurs even in this small case.
UID:154655-21918147@events.umich.edu
URL:https://events.umich.edu/event/154655
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 2866
CONTACT:
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