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DTSTART:20230312T070000
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DTSTART;TZID=America/Toronto:20240118T143000
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URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/extendin
 g-torelli-map-alternative-compactifications-moduli
SUMMARY:Extending the torelli map to alternative compactifications of the\n
 moduli space of curves
CLASS:PUBLIC
DESCRIPTION:CHANGHO HAN\, DEPARTMENT OF PURE MATHEMATICS\, UNIVERSITY OF WA
 TERLOO\n\nIt is well-known that the Torelli map\, that turns a smooth curv
 e of\ngenus g into its Jacobian (a principally polarized abelian variety o
 f\ndimension g)\, extends to a map from the Deligne—Mumford moduli of\ns
 table curves to the moduli of semi-abelic varieties by Alexeev.\nMoreover\
 , it is also known that the Torelli map does not extend over\nthe alternat
 ive compactifications of the moduli of curves as described\nby the Hassett
 —Keel program\, including the moduli of pseudostable\ncurves (can have n
 odes and cusps but not elliptic tails). But it is\nnot yet known whether t
 he Torelli map extends over alternative\ncompactifications of the moduli o
 f curves described by Smyth\; what\nabout the moduli of curves of genus g 
 with rational m-fold\nsingularities\, where m is a positive integer bounde
 d above? As a joint\nwork in progress with Jesse Kass and Matthew Satriano
 \, I will describe\nmoduli spaces of curves with m-fold singularities (wit
 h topological\nconstraints) and describe how far the Torelli map extends o
 ver such\nspaces into the Alexeev compactifications.\n\nMC 5417
DTSTAMP:20260318T202856Z
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