Infinitesimal structure of BunG


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


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


          @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


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.


Zoom link