Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve

Let \(X\) be a smooth projective curve over a field of characteristic zero and let \(D\) be a non-empty set of rational points of \(X\). We calculate the motivic classes of moduli stacks of semistable parabolic bundles with connections on \((X,D)\) and motivic classes of moduli stacks of semistable...

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Bibliographic Details
Published in:arXiv.org 2020-07
Main Authors: Fedorov, Roman, Soibelman, Alexander, Soibelman, Yan
Format: Article
Language:English
Subjects:
Bundles
Bundling
Stacks
Online Access:Get full text
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Summary:Let \(X\) be a smooth projective curve over a field of characteristic zero and let \(D\) be a non-empty set of rational points of \(X\). We calculate the motivic classes of moduli stacks of semistable parabolic bundles with connections on \((X,D)\) and motivic classes of moduli stacks of semistable parabolic Higgs bundles on \((X,D)\). As a by-product we give a criteria for non-emptiness of these moduli stacks, which can be viewed as a version of the Deligne-Simpson problem.
ISSN:2331-8422
DOI:10.48550/arxiv.1910.12348