On finite generation of the section ring of the determinant of cohomology line bundle

P. Belkale; A. Gibney

doi:10.1090/tran/7564

On finite generation of the section ring of the determinant of cohomology line bundle

P. Belkale, A. Gibney

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

For C a stable curve of arithmetic genus g ≥ 2 and D the determinant of cohomology line bundle on Bun_SL(r)(C), we show that the section ring for the pair (Bun_SL(r)(C),D) is finitely generated. Applications involving vector bundles of conformal blocks are given, including quasi polynomiality at the level of the Chern character of the bundles on M_g.

Original language	English (US)
Pages (from-to)	7199-7242
Number of pages	44
Journal	Transactions of the American Mathematical Society
Volume	371
Issue number	10
DOIs	https://doi.org/10.1090/tran/7564
State	Published - 2019

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/tran/7564

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abstract = "For C a stable curve of arithmetic genus g ≥ 2 and D the determinant of cohomology line bundle on BunSL(r)(C), we show that the section ring for the pair (BunSL(r)(C),D) is finitely generated. Applications involving vector bundles of conformal blocks are given, including quasi polynomiality at the level of the Chern character of the bundles on Mg.",

author = "P. Belkale and A. Gibney",

note = "Funding Information: Received by the editors June 11, 2017, and, in revised form, February 25, 2018. 2010 Mathematics Subject Classification. Primary 14H60, 14D20; Secondary 14L24, 81T40. The second author was supported by NSF DMS-1201268 and DMS-1344994. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

year = "2019",

doi = "10.1090/tran/7564",

language = "English (US)",

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T1 - On finite generation of the section ring of the determinant of cohomology line bundle

AU - Belkale, P.

AU - Gibney, A.

N1 - Funding Information: Received by the editors June 11, 2017, and, in revised form, February 25, 2018. 2010 Mathematics Subject Classification. Primary 14H60, 14D20; Secondary 14L24, 81T40. The second author was supported by NSF DMS-1201268 and DMS-1344994. Publisher Copyright: © 2019 American Mathematical Society.

PY - 2019

Y1 - 2019

N2 - For C a stable curve of arithmetic genus g ≥ 2 and D the determinant of cohomology line bundle on BunSL(r)(C), we show that the section ring for the pair (BunSL(r)(C),D) is finitely generated. Applications involving vector bundles of conformal blocks are given, including quasi polynomiality at the level of the Chern character of the bundles on Mg.

AB - For C a stable curve of arithmetic genus g ≥ 2 and D the determinant of cohomology line bundle on BunSL(r)(C), we show that the section ring for the pair (BunSL(r)(C),D) is finitely generated. Applications involving vector bundles of conformal blocks are given, including quasi polynomiality at the level of the Chern character of the bundles on Mg.

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 10

ER -

On finite generation of the section ring of the determinant of cohomology line bundle

Abstract

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