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Stability of the parabolic Poincaré bundle

Suratno Basu

Institute of Mathematical Sciences, HBNI, CIT Campus, Tharamani, Chennai 600113, India

E-mail Address: suratnob@imsc.res.in

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Indranil Biswas

School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 4000005, India

E-mail Address: indranil@math.tifr.res.in

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, and

Krishanu Dan

Chennai Mathematical Institute, H1 Sipcot IT Park, Siruseri, Kelambakkam 603103, India

E-mail Address: krishanud@cmi.ac.in

Corresponding author.

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https://doi.org/10.1142/S0219887818500810Cited by:1 (Source: Crossref)

Abstract

Given a compact Riemann surface $X$ and a moduli space $M_{α} (Λ)$ of parabolic stable bundles on it of fixed determinant of complete parabolic flags, we prove that the Poincaré parabolic bundle on $X \times M_{α} (Λ)$ is parabolic stable with respect to a natural polarization on $X \times M_{α} (Λ)$ .

Keywords:

AMSC: 14H60, 14D20

References

1. V. Balaji, L. Brambila-Paz and P. E. Newstead, Stability of the Poincaré bundle, Math. Nachr. 188 (1997) 5–15. Crossref, Web of Science, Google Scholar
2. I. Biswas and A. Dey, Brauer group of a moduli space of parabolic vector bundles over a curve, J. K-Theory 8 (2011) 437–449. Crossref, Google Scholar
3. I. Biswas, T. L. Gómez and N. Hoffmann, Stability of the Poincaré bundle, preprint (2017), arXiv:1701.04649. Google Scholar
4. I. Biswas and N. Raghavendra, Determinants of parabolic bundles on Riemann surfaces, Proc. Indian Acad. Sci. (Math. Sci.) 103 (1993) 41–71. Crossref, Web of Science, Google Scholar
5. H. U. Boden and K. Yokogawa, Rationality of moduli spaces of parabolic bundles, J. London Math. Soc. 59 (1999) 461–478. Crossref, Web of Science, Google Scholar
6. O. García-Prada, P. B. Gothen and V. Muñoz, Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, Mem. Amer. Math. Soc. 187 (2007) 879. Web of Science, Google Scholar
7. T. L. Gomez and M. Logares, A Torelli theorem for the moduli space of parabolic higgs bundles, Adv. Geom. 11 (2011) 429–444. Crossref, Web of Science, Google Scholar
8. A. Kouvidakis and T. Pantev, The automorphism group of the moduli space of semi stable vector bundles, Math. Ann. 302 (1995) 225–268. Crossref, Web of Science, Google Scholar
9. Y. Li, Spectral curves, theta divisors and picard bundles, Int. J. Math. 2 (1991) 525–550. Link, Google Scholar
10. V. B. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980) 205–239. Crossref, Web of Science, Google Scholar
11. M. S. Narasimhan and T. R. Ramadas, Factorisation of generalised theta functions. I, Invent. Math. 114 (1993) 565–623. Crossref, Web of Science, Google Scholar
12. X. Sun, Degeneration of moduli spaces and generalized theta functions, J. Algebraic Geom. 9 (2000) 459–527. Web of Science, Google Scholar