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X-WR-CALNAME:Center for Complex Geometry
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20210101T000000
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DTSTART;TZID=Asia/Seoul:20210916T110000
DTEND;TZID=Asia/Seoul:20210916T120000
DTSTAMP:20210924T085233
CREATED:20210916T020000Z
LAST-MODIFIED:20210826T030047Z
UID:655-1631790000-1631793600@ccg.ibs.re.kr
SUMMARY:Changho Han\, Compact Moduli of Lattice Polarized K3 Surfaces with Nonsymplectic Cyclic Action of Order 3
DESCRIPTION: Speaker\n\n\nChangho Han\nUniversity of Georgia\n\n\n\n\n\n\nObserve that any construction of “meaningful” compactification of moduli spaces of objects involve enlarging the class of objects in consideration. For example\, Deligne and Mumford introduced the notion of stable curves in order to compactify the moduli of smooth curves of genus g\, and Satake used the periods from Hodge theory to compactify the same moduli space. After a brief review of the elliptic curve case (how those notions are the same)\, I will generalize into looking at various compactifications of Kondo’s moduli space of lattice polarized K3 surfaces (which are of degree 6) with nonsymplectic Z/3Z group action; this involves periods and genus 4 curves by Kondo’s birational period map in 2002. Then\, I will extend Kondo’s birational map to describe birational relations between different compactifications by using the slc compactifications (also known as KSBA compactifications) of moduli of surface pairs. The main advantage of this approach is that we obtain an explicit classification of degenerate K3 surfaces\, which is used to find geometric meaning of points parametrized by Hodge-theoretic compactifications. This comes from joint works (in progress) with Valery Alexeev\, Anand Deopurkar\, and Philip Engel.
URL:https://ccg.ibs.re.kr/event/2021-09-16/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
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