Changho Han (University of Waterloo)
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Title: Extending Torelli map from Smyth's alternative compactifications of the moduli of curves
Abstract: It is well-known that the Torelli map, that turns a smooth curve of genus g into its Jacobian (a principally polarized abelian variety of dimension g), extends to a map from the Deligne鈥擬umford moduli of stable curves to the moduli of semi-abelic varieties by Alexeev. Moreover, it is also known that the Torelli map does not extend over the alternative compactifications of the moduli of curves as described by the Hassett鈥擪eel program, including the moduli of pseudostable curves (can have nodes and cusps but not elliptic tails).
But it is not yet known whether the Torelli map extends over the Smyth's alternative compactifications of the moduli of curves; what about the moduli of curves of genus g with rational m-fold singularities, where m is a positive integer bounded above? As a joint work in progress with Jesse Kass and Matthew Satriano, I will describe two types of moduli of curves with m-fold singularities and describe how far the Torelli map
extends over such spaces into the Alexeev compactifications.
In person听UQAM PK-5675
Zoom meeting 86352363947