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Tuesday Seminar on Topology
Seminar information archive ～04/09｜Next seminar｜Future seminars 04/10～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
2012/06/19
17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)
Yukio Matsumoto (Gakushuin University)
On the universal degenerating family of Riemann surfaces
over the D-M compactification of moduli space (JAPANESE)
Yukio Matsumoto (Gakushuin University)
On the universal degenerating family of Riemann surfaces
over the D-M compactification of moduli space (JAPANESE)
[ Abstract ]
It is usually understood that over the Deligne-
Mumford compactification of moduli space of Riemann surfaces of
genus > 1, there is a family of stable curves. However, if one tries to
construct this family precisely, he/she must first take a disjoint union
of various types of smooth families of stable curves, and then divide
them by their automorphisms to paste them together. In this talk we will
show that once the smooth families are divided, the resulting quotient
family contains not only stable curves but virtually all types of
degeneration of Riemann surfaces, becoming a kind of universal
degenerating family of Riemann surfaces.
It is usually understood that over the Deligne-
Mumford compactification of moduli space of Riemann surfaces of
genus > 1, there is a family of stable curves. However, if one tries to
construct this family precisely, he/she must first take a disjoint union
of various types of smooth families of stable curves, and then divide
them by their automorphisms to paste them together. In this talk we will
show that once the smooth families are divided, the resulting quotient
family contains not only stable curves but virtually all types of
degeneration of Riemann surfaces, becoming a kind of universal
degenerating family of Riemann surfaces.
