

Iskovskikh Seminar
May 26, 2016 18:00, Moscow, Steklov Mathematical Institute, room 540






On noncommutative rigidity of the moduli stack of stable pointed curves
Shinnosuke Okawa^{} ^{} Department of Mathematics, Graduate School of Science, Osaka University

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Abstract:
As the first nontrivial case of
the Kapranov's geometric syzygy principle, Hacking proved that the
GrothendieckKnudsen moduli stack of stable $n$pointed genus $g$curves
is rigid for any $(g, n)$. In this talk we show that the $2$nd
Hochschild cohomology of the moduli space is trivial when $g=0$ except
the case $n=5$, which implies the rigidity of the abelian category of
coherent sheaves on the moduli space. We will also explain what is
known for the case $g>0$ and the remaining issues. This is a joint
work in progress with Taro Sano.
Language: English

