Details
| Original language | English |
|---|---|
| Pages (from-to) | 1034-1061 |
| Number of pages | 28 |
| Journal | Canadian journal of mathematics |
| Volume | 74 |
| Issue number | 4 |
| Early online date | 21 Apr 2021 |
| Publication status | Published - 21 Aug 2022 |
Abstract
Given a compact Kähler manifold X, it is shown that pairs of the form, where E is a trivial holomorphic vector bundle on X, and D is an integrable holomorphic connection on E, produce a neutral Tannakian category. The corresponding pro-Algebraic affine group scheme is studied. In particular, it is shown that this pro-Algebraic affine group scheme for a compact Riemann surface determines uniquely the isomorphism class of the Riemann surface.
Keywords
- complex torus, Integrable holomorphic connection,Higgs bundle, neutral Tannakian category, Torelli theorem
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Canadian journal of mathematics, Vol. 74, No. 4, 21.08.2022, p. 1034-1061.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On certain Tannakian categories of integrable connections over Kähler manifolds
AU - Biswas, Indranil
AU - Dos Santos, João Pedro
AU - Dumitrescu, Sorin
AU - Heller, Sebastian
N1 - Funding Information: The first- and third-named authors were partially supported by the French government through the UCAJEDI Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR2152IDEX201. The first-named author is partially supported by a J. C. Bose Fellowship, and school of mathematics, TIFR, is supported by 12-R&D-TFR-5.01-0500. The fourth-named author is supported by the DFG grant HE 6829/3-1 of the DFG priority program SPP 2026 Geometry at Infinity. Acknowledgment: We would like to thank the referees for their helpful comments. We would also like to thank Carlos Simpson for a useful discussion. The first- and third-named authors would like to thank the International Center for Theoretical Sciences, Bengaluru, India, for hospitality.
PY - 2022/8/21
Y1 - 2022/8/21
N2 - Given a compact Kähler manifold X, it is shown that pairs of the form, where E is a trivial holomorphic vector bundle on X, and D is an integrable holomorphic connection on E, produce a neutral Tannakian category. The corresponding pro-Algebraic affine group scheme is studied. In particular, it is shown that this pro-Algebraic affine group scheme for a compact Riemann surface determines uniquely the isomorphism class of the Riemann surface.
AB - Given a compact Kähler manifold X, it is shown that pairs of the form, where E is a trivial holomorphic vector bundle on X, and D is an integrable holomorphic connection on E, produce a neutral Tannakian category. The corresponding pro-Algebraic affine group scheme is studied. In particular, it is shown that this pro-Algebraic affine group scheme for a compact Riemann surface determines uniquely the isomorphism class of the Riemann surface.
KW - complex torus
KW - Integrable holomorphic connection,Higgs bundle
KW - neutral Tannakian category
KW - Torelli theorem
UR - http://www.scopus.com/inward/record.url?scp=85119118399&partnerID=8YFLogxK
U2 - 10.4153/S0008414X21000201
DO - 10.4153/S0008414X21000201
M3 - Article
AN - SCOPUS:85119118399
VL - 74
SP - 1034
EP - 1061
JO - Canadian journal of mathematics
JF - Canadian journal of mathematics
SN - 0008-414X
IS - 4
ER -