Koszul's Splitting Theorem and the Super Atiyah Class

Autor:	Bettadapura, Kowshik
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematical Physics 32C11 32C35 58A50
Druh dokumentu:	Working Paper
Popis:	In this article we present a self-contained account of two important results in complex supergeometry: (1) Koszul's Splitting theorem and (2) Donagi and Witten's decomposition of the super Atiyah class. These results are related in the same sense that global holomorphic connections on a holomorphic vector bundle are `related' to the Atiyah class of that vector bundle---the latter being the obstruction to the existence of the former. In complex supergeometry: Koszul's theorem pertains to the existence of supermanifold splittings whereas the super Atiyah class accordingly pertains to obstructions to the existence of splittings. Comment: 91 pages, comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.00177 Zobrazit plný text záznamu View this record from Arxiv