# Infinitesimal structure of BunG

### APA

Grantcharov, N. (2024). Infinitesimal structure of BunG. Perimeter Institute. https://pirsa.org/24050090

### MLA

Grantcharov, Nikolay. Infinitesimal structure of BunG. Perimeter Institute, May. 23, 2024, https://pirsa.org/24050090

### BibTex

@misc{ pirsa_PIRSA:24050090, doi = {10.48660/24050090}, url = {https://pirsa.org/24050090}, author = {Grantcharov, Nikolay}, keywords = {Mathematical physics}, language = {en}, title = {Infinitesimal structure of BunG}, publisher = {Perimeter Institute}, year = {2024}, month = {may}, note = {PIRSA:24050090 see, \url{https://pirsa.org}} }

Nikolay Grantcharov University of Chicago

## Abstract

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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