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Globally F-regular type of moduli spaces

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We prove that moduli spaces of semistable parabolic bundles and generalized parabolic sheaves with fixed determinant on a smooth projective curve are of globally F-regular type.

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  1. Brion, M., Kumar, S.: Frobenius Splitting Methods in Geometry and Representation Theory, Progress in Mathematics, 231. Birkhäuser, Boston (2005)

    Book  Google Scholar 

  2. Grothendieck, A.: EGA IV. Publ. IHES 28, 5–255 (1966)

    Article  Google Scholar 

  3. Knop, F.: Der kanonische moduleines invariantenrings. J. Algebra 127, 40–54 (1989)

    Article  MathSciNet  Google Scholar 

  4. Kumar, S., Lauritzen, N., Thomsen, J.F.: Frobenius splitting of cotangent bundles of flag varieties. Invent. Math. 136, 603–621 (1999)

    Article  MathSciNet  Google Scholar 

  5. Lauritzen, N., Raben-Pedersen, U., Thomsen, J.F.: Global F-regularity of Schubert varieties with applications to D-modules. J. Am. Math. Soc. 19, 345–355 (2006)

    Article  MathSciNet  Google Scholar 

  6. Mehta, V.B., Ramadas, T.R.: Moduli of vector bundles, Frobenius splitting, and invariant theory. Ann. Math. 144, 269–313 (1996)

    Article  MathSciNet  Google Scholar 

  7. Mehta, V.B., Ramanathan, A.: Frobenius splitting and cohomology vanishing for Schubert varieties. Ann. Math. 122, 27–40 (1985)

    Article  MathSciNet  Google Scholar 

  8. Mehta, V.B., Ramanathan, A.: Schubert varieties in \(G/B\times G/B\). Compos. Math. 67, 355–358 (1988)

    MATH  Google Scholar 

  9. Mumford, D., Fogarty, J., Kirwan, F.: Geometric Invariant Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, 34. SpringerBerlin, Berlin (1994)

    Google Scholar 

  10. Mustata, M., Srinivas, V.: Ordinary varieties and the comparison between multiplier ideals and test ideals. Nagoya Math. J. 204, 125–157 (2011)

    Article  MathSciNet  Google Scholar 

  11. Narasimhan, M.S., Ramadas, T.R.: Factorisation of generalised theta functions I. Invent. Math. 114, 217–235 (1993)

    Article  MathSciNet  Google Scholar 

  12. Pauly, C.: Espaces de modules de fibrés paraboliques et blocs conformes. Duke Math. J. 84, 565–623 (1996)

    Article  MathSciNet  Google Scholar 

  13. Ramanan, S., Ramanathan, A.: Projective normality of flag varieties and Schubert varieties. Invent. Math. 79, 217–224 (1985)

    Article  MathSciNet  Google Scholar 

  14. Schwede, K., Smith, K.E.: Globally F-regular and log Fano varieties. Adv. Math. 224, 863–894 (2010)

    Article  MathSciNet  Google Scholar 

  15. Seshadri, C.S.: Geometric reductivity over arbitrary base. Adv. Math. 26, 225–274 (1977)

    Article  MathSciNet  Google Scholar 

  16. Smith, K.E.: Globally F-regular varieties: applications to vanishing theorems for quotients of Fano varieties. Mich. Math J. 48, 553–572 (2000)

    Article  MathSciNet  Google Scholar 

  17. Sun, X.: Degeneration of moduli spaces and generalized theta functions. J. Algebr. Geometry 9, 459–527 (2000)

    MathSciNet  MATH  Google Scholar 

  18. Sun, X.: Factorization of generalized theta functions in the reducible case. Ark. Mat. 41, 165–202 (2003)

    Article  MathSciNet  Google Scholar 

  19. Sun, X.: Factorization of generalized theta functions revisited. Algebra Colloquium. 24(1), 1–52 (2017)

    Article  MathSciNet  Google Scholar 

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Xiaotao Sun would like to thank C. S. Seshadri for a number of emails of discussions about Lemma 2.9, and he also would like to thank K. Schwede and K. E. Smith for discussions (by emails) of globally F-regular type varieties.

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Correspondence to Xiaotao Sun.

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Communicated by Vasudevan Srinivas.

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Both authors are supported by the National Natural Science Foundation of China No.11831013 and No.11921001; Mingshuo Zhou is also supported by the National Natural Science Foundation of China No.11501154.

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Sun, X., Zhou, M. Globally F-regular type of moduli spaces. Math. Ann. 378, 1245–1270 (2020).

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