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

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Alfaya, D (Author) Other; Oliveira, A (Author) FCUP

Journal

Title: Journal of Geometry and Physics

Vol. 201

ISSN: 0393-0440

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-010-AFN

DOI: 10.1016/j.geomphys.2024.105195

Abstract (EN): Let L = (L, [ , ], 8) be an algebraic Lie algebroid over a smooth projective curve X of genus g >= 2 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 L-connections of rank r and degree d over X does not depend on the Lie algebroid structure [ , ] and 8 of L 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 KX(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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 55