Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces

DOI10.1016/J.GEOMPHYS.2024.105195arXiv2102.12246MaRDI QIDQ6505066

Author name not available (Why is that?)

Abstract: Let $mathcalL=(L,[cdot,,cdot],delta)$ be an algebraic Lie algebroid over a smooth projective curve of genus $ggeq2$ such that $L$ is a line bundle whose degree is less than $2-2g$. Let $r$ and $d$ be coprime numbers. We prove that the motivic class of the moduli space of $mathcalL$-connections of rank $r$ and degree $d$ over $X$ does not depend on the Lie algebroid structure $[cdot,,cdot]$ and $delta$ of $mathcalL$ and neither on the line bundle $L$ itself, but only on the degree of $L$ (and of course on $r$, $d$ and $X$). In particular it is equal to the motivic class of the moduli space of $K_X(D)$-twisted Higgs bundles of rank $r$ and degree $d$, for $D$ any effective divisor with the appropriate degree. As a consequence, similar results (actually slightly stronger) are obtained for the corresponding $E$-polynomials. Some applications of these results are then deduced.

This page was built for publication: Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6505066)