Generalized B-Opers
Generalized B-Opers
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DOI：
10.3842/sigma.2020.041
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
I. Biswas;L. Schaposnik;Mengxue Yang
中科院分区：
文献类型：
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作者：
I. Biswas;L. Schaposnik;Mengxue Yang
Beilinson-Drinfeld [arXiv：math.AG/0501398]介绍了歌剧。在[J.Math.PuresAppl.82（2003），1-42]中，考虑了更高秩的类似物，其中允许操作过滤的连续子具有更高秩。本文引入并研究了广义$B$-算子（其中“$B$”代表“双线性”），它是通过赋予基本向量丛一个与滤子和联络相容的双线性形式而得到的。特别是，我们研究这些B$-opers的结构，通过考虑这些结构与射流束和黎曼曲面上的几何结构的关系。
Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We dedicate this paper to introducing and studying generalized $B$-opers (where "$B$" stands for "bilinear"), obtained by endowing the underlying vector bundle with a bilinear form which is compatible with both the filtration and the connection. In particular, we study the structure of these $B$-opers, by considering the relationship of these structures with jet bundles and with geometric structures on a Riemann surface.