Details
| Original language | English |
|---|---|
| Pages (from-to) | 8311-8355 |
| Number of pages | 45 |
| Journal | International Mathematics Research Notices |
| Volume | 2023 |
| Issue number | 10 |
| Early online date | 20 Apr 2022 |
| Publication status | Published - May 2023 |
Abstract
Branched projective structures were introduced by Mandelbaum [22, 23], and opers were introduced by Beilinson and Drinfeld [2, 3]. We define the branched analog of -opers and investigate their properties. For the usual -opers, the underlying holomorphic vector bundle is actually determined uniquely up to tensoring with a holomorphic line bundle of order. For the branched -opers, the underlying holomorphic vector bundle depends more intricately on the oper. While the holomorphic connection for a branched -oper is nonsingular, given a branched -oper, we associate to it a certain holomorphic vector bundle equipped with a logarithmic connection. This holomorphic vector bundle in question supporting a logarithmic connection does not depend on the branched oper. We characterize the branched -opers in terms of the logarithmic connections on this fixed holomorphic vector bundle.
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In: International Mathematics Research Notices, Vol. 2023, No. 10, 05.2023, p. 8311-8355.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Branched SL(r, ℂ)-Opers
AU - Biswas, Indranil
AU - Dumitrescu, Sorin
AU - Heller, Sebastian
N1 - Publisher Copyright: © 2022 The Author(s).
PY - 2023/5
Y1 - 2023/5
N2 - Branched projective structures were introduced by Mandelbaum [22, 23], and opers were introduced by Beilinson and Drinfeld [2, 3]. We define the branched analog of -opers and investigate their properties. For the usual -opers, the underlying holomorphic vector bundle is actually determined uniquely up to tensoring with a holomorphic line bundle of order. For the branched -opers, the underlying holomorphic vector bundle depends more intricately on the oper. While the holomorphic connection for a branched -oper is nonsingular, given a branched -oper, we associate to it a certain holomorphic vector bundle equipped with a logarithmic connection. This holomorphic vector bundle in question supporting a logarithmic connection does not depend on the branched oper. We characterize the branched -opers in terms of the logarithmic connections on this fixed holomorphic vector bundle.
AB - Branched projective structures were introduced by Mandelbaum [22, 23], and opers were introduced by Beilinson and Drinfeld [2, 3]. We define the branched analog of -opers and investigate their properties. For the usual -opers, the underlying holomorphic vector bundle is actually determined uniquely up to tensoring with a holomorphic line bundle of order. For the branched -opers, the underlying holomorphic vector bundle depends more intricately on the oper. While the holomorphic connection for a branched -oper is nonsingular, given a branched -oper, we associate to it a certain holomorphic vector bundle equipped with a logarithmic connection. This holomorphic vector bundle in question supporting a logarithmic connection does not depend on the branched oper. We characterize the branched -opers in terms of the logarithmic connections on this fixed holomorphic vector bundle.
UR - http://www.scopus.com/inward/record.url?scp=85161015814&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnac090
DO - 10.1093/imrn/rnac090
M3 - Article
AN - SCOPUS:85161015814
VL - 2023
SP - 8311
EP - 8355
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 10
ER -