All Questions

Let $E\rightarrow X$ be a vector bundle and let $\mathcal{A}$ denote the space of connections on $E$. Pulling back $E$ by the second projection we obtain a vector bundle $\mathbb{E}=p_2^*E\rightarrow ...

Let $\mathcal X \rightarrow S$ be a flat family of projective varieties over a discrete valuation ring $S$ such that the generic fibre $\mathcal X_{\eta}$ (say) is smooth projective variety and the ...

Let $\mathcal{M}_{d}(G)$ be the moduli space of $G$-Higgs bundles. $\mathcal{M}_{d}(G)$ have a non-trivial $\mathbb{C}^{*}$-holomorphic action by multiplication of the Higgs field, $$ z\cdot (E, \...

Isomorphism classes of line bundles over a scheme $X$ are described by the Picard group $Pic(X)$. Now there is a paper that describes the moduli space of line bundles with connections. This paper is ...

Let $\mathcal{M}_g$ be the moduli space of curves of genus $g$. Consider the holomorphic bundle $\mathcal{H}^k\rightarrow\mathcal{M}_g$ whose fiber over a curve $C\in\mathcal{M}_g$ is the space of ...