Motivic classes of irregular Higgs bundles and irregular connections on a curve
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909179794423808 |
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| author | Fedorov, Roman Soibelman, Alexander Soibelman, Yan |
| author_facet | Fedorov, Roman Soibelman, Alexander Soibelman, Yan |
| contents | Let $X$ be a smooth projective curve over a field of characteristic zero and let $\mathcal D$ be an effective divisor on $X$. We calculate motivic classes of various moduli stacks of parabolic vector bundles with irregular connections on $X$ and of irregular parabolic Higgs bundles on $X$ with poles bounded by $\mathcal D$ and with fully or partially fixed formal normal forms. Along the way, we obtain several results about irregular connections and irregular parabolic Higgs bundles. In particular, we give a criterion for the existence of a connection on a higher level parabolic bundle and also develop homological algebra for irregular connections and irregular parabolic Higgs bundles. We also simplify our previous results in the regular case by re-writing the formulas for motivic classes in terms of the HLV generating function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Motivic classes of irregular Higgs bundles and irregular connections on a curve Fedorov, Roman Soibelman, Alexander Soibelman, Yan Algebraic Geometry High Energy Physics - Theory Mathematical Physics K-Theory and Homology Symplectic Geometry Let $X$ be a smooth projective curve over a field of characteristic zero and let $\mathcal D$ be an effective divisor on $X$. We calculate motivic classes of various moduli stacks of parabolic vector bundles with irregular connections on $X$ and of irregular parabolic Higgs bundles on $X$ with poles bounded by $\mathcal D$ and with fully or partially fixed formal normal forms. Along the way, we obtain several results about irregular connections and irregular parabolic Higgs bundles. In particular, we give a criterion for the existence of a connection on a higher level parabolic bundle and also develop homological algebra for irregular connections and irregular parabolic Higgs bundles. We also simplify our previous results in the regular case by re-writing the formulas for motivic classes in terms of the HLV generating function. |
| title | Motivic classes of irregular Higgs bundles and irregular connections on a curve |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics K-Theory and Homology Symplectic Geometry |
| url | https://arxiv.org/abs/2404.14549 |