Motivic classes of Higgs bundles and of bundles with connections
演讲者
Roman Fedorov
时间
2025年03月20日 10:00 至 11:00
地点
A6-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
Let $X$ be a smooth geometrically connected projective curve over a field $k$. Consider the moduli stacks $Higgs_{r,d}(X)$ of rank $r$ degree d Higgs bundles on $X$. When $k$ is a finite field, O. Schiffmann and S. Mozgovoy calculated the volumes of the semistable parts of these stacks. Their formulas were significantly simplified by A. Mellit.
In a joint work with A. Soibelman and Y. Soibelman, the speaker has calculated the motivic volume of the above stacks when k has characteristic zero. We also calculated the motivic volumes of the stacks $Conn_r(X)$ of rank $r$ vector bundles with connections. We extended these results to the case of Higgs bundles with connections with singularities (including generic irregular singularities). I will discuss these results and give a brief overview of the strategies of
the proofs.
In a joint work with A. Soibelman and Y. Soibelman, the speaker has calculated the motivic volume of the above stacks when k has characteristic zero. We also calculated the motivic volumes of the stacks $Conn_r(X)$ of rank $r$ vector bundles with connections. We extended these results to the case of Higgs bundles with connections with singularities (including generic irregular singularities). I will discuss these results and give a brief overview of the strategies of
the proofs.