Infinitesimal structure of BunG

PIRSA ID: 24050090
Event Type: Seminar
Scientific Area(s):
Mathematical Physics
End date:
  • Nikolay Grantcharov, University of Chicago

Given a semisimple group G and a smooth projective curve X over an algebraically closed field of arbitrary characteristic, let Bun_G(X) denote the moduli space of principal G-bundles over X. For a bundle P without infinitesimal symmetries, we describe the n^th order divided-power infinitesimal jet spaces of Bun_G(X) at P for each n. The description is in terms of differential forms on X^n with logarithmic singularities along the diagonals. Furthermore, we show the pullback of these differential forms to the Fulton-Macpherson compactification space is an isomorphism, thus illustrating a connection between infinitesimal jet spaces of Bun_G(X) and the Lie operad.


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