Motivic classes of moduli of Higgs bundles and moduli of bundles with connections

Fedorov, Roman; Soibelman, Alexander; Soibelman, Yan

doi:10.48550/arxiv.1705.04890

Cited by 5 publications

(24 citation statements)

References 15 publications

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“…Our formulas for motivic classes of the moduli stacks above are all given in terms of certain motivic classes B γ called motivic Donaldson-Thomas invariants (see Section 1.5 for this terminology), which we are going to define. First of all, we recall that in [FSS,Sect. 2] we defined (following earlier works [Eke1,Sect.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…For a curve X and a partition λ we defined the series J mot λ (z), H mot λ (z) ∈ Mot(k) [[z]] in [FSS,Sect. 1.3.2].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…The corresponding equivalence classes are called points of S; the set of points is denoted by |S|. See [FSS,Sect. 2] for more details.…”

Section: Preliminariesmentioning

confidence: 99%

“…Motivic functions and motivic classes. Recall that in [FSS,Sect. 2] we defined (following [Eke1, Sect.…”

Section: Preliminariesmentioning

confidence: 99%

“…Finally we note that the general philosophy of Donaldson-Thomas invariants and the approach via motivic and cohomological Hall algebras (see [KS1,KS2]) are applicable to our situation. For more details about the approach that uses motivic Hall algebras we refer the reader to [FSS,Sect. 1.6,Rem.…”

mentioning

confidence: 99%

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

Fedorov,

Soibelman,

Soibelman

2019

Preprint

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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 when these moduli stacks are non-empty, which can be viewed as a version of Deligne-Simpson problem.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

“…For a curve X and a partition λ we defined the series J mot λ (z), H mot λ (z) ∈ Mot(k) [[z]] in [FSS,Sect. 1.3.2].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…The corresponding equivalence classes are called points of S; the set of points is denoted by |S|. See [FSS,Sect. 2] for more details.…”

Section: Preliminariesmentioning

confidence: 99%

“…Motivic functions and motivic classes. Recall that in [FSS,Sect. 2] we defined (following [Eke1, Sect.…”

Section: Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

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

Fedorov,

Soibelman,

Soibelman

2019

Preprint

Self Cite

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

Fedorov¹,

Soibelman²,

Soibelman³

2020

SIGMA

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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.

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Counting twisted Higgs bundles

Mozgovoy

Ronan

2022

Mathematical Research Letters

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Motivic classes of moduli of Higgs bundles and moduli of bundles with connections

Cited by 5 publications

References 15 publications

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

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

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

Counting twisted Higgs bundles

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