Principal bundles with parabolic structure
Authors:
V. Balaji, I. Biswas and D. S. Nagaraj
Journal:
Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 37-44
MSC (2000):
Primary 14F05; Secondary 32L05
DOI:
https://doi.org/10.1090/S1079-6762-01-00092-0
Published electronically:
April 24, 2001
MathSciNet review:
1826994
Full-text PDF Free Access
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Abstract: We define a principal bundle analog of vector bundles with parabolic structure over a normal crossing divisor. Various results on parabolic vector bundles and usual principal bundles are extended to the context of parabolic principal bundles.
BBN1 V. Balaji, I. Biswas and D. S. Nagaraj, Principal bundles over projective manifolds with parabolic structure over a divisor, Tohoku Math. J. (to appear).
BBN2 V. Balaji, I. Biswas and D. S. Nagaraj, in preparation.
- Indranil Biswas, Parabolic ample bundles, Math. Ann. 307 (1997), no. 3, 511–529. MR 1437053, DOI https://doi.org/10.1007/s002080050048
- Indranil Biswas, Parabolic bundles as orbifold bundles, Duke Math. J. 88 (1997), no. 2, 305–325. MR 1455522, DOI https://doi.org/10.1215/S0012-7094-97-08812-8
- Indranil Biswas, Chern classes for parabolic bundles, J. Math. Kyoto Univ. 37 (1997), no. 4, 597–613. MR 1625964, DOI https://doi.org/10.1215/kjm/1250518206
- Pierre Deligne, James S. Milne, Arthur Ogus, and Kuang-yen Shih, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Mathematics, vol. 900, Springer-Verlag, Berlin-New York, 1982. MR 654325
- Yujiro Kawamata, Katsumi Matsuda, and Kenji Matsuki, Introduction to the minimal model problem, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 283–360. MR 946243, DOI https://doi.org/10.2969/aspm/01010283
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BBN1 V. Balaji, I. Biswas and D. S. Nagaraj, Principal bundles over projective manifolds with parabolic structure over a divisor, Tohoku Math. J. (to appear).
BBN2 V. Balaji, I. Biswas and D. S. Nagaraj, in preparation.
Bi1 I. Biswas, Parabolic ample bundles, Math. Ann. 307 (1997), 511–529.
Bi2 I. Biswas, Parabolic bundles as orbifold bundles, Duke Math. J. 88 (1997), 305–325.
Bi3 I. Biswas, Chern classes for parabolic bundles, J. Math. Kyoto Univ. 37 (1997), 597–613.
DM P. Deligne and J. Milne, Tannakian Categories, “Hodge Cycles, Motives and Shimura Varieties”, Springer Lect. Notes Math. 900 (1989), 101–228.
KMM Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, Adv. Stud. Pure Math. 10 (1987), 283–360.
MS V. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structure, Math. Ann. 248 (1980), 205–239.
MY M. Maruyama and K. Yokogawa, Moduli of parabolic stable sheaves, Math. Ann. 293 (1992), 77–99.
No1 M. V. Nori, On the representations of the fundamental group, Comp. Math. 33 (1976), 29–41.
No2 M. V. Nori, The fundamental group scheme, Proc. Indian Acad. Sci. Math. Sci. 91 (1982), 73–122.
RR S. Ramanan and A. Ramanathan, Some remarks on the instability flag, Tôhoku Math. J. 36 (1984), 269–291.
Yo K. Yokogawa, Infinitesimal deformations of parabolic Higgs sheaves, Int. J. Math. 6 (1995), 125–148.
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Additional Information
V. Balaji
Affiliation:
Institute of Mathematical Sciences, C.I.T. Campus, Taramani Chennai 600113, India
Email:
vbalaji@imsc.ernet.in
I. Biswas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
MR Author ID:
340073
Email:
indranil@math.tifr.res.in
D. S. Nagaraj
Affiliation:
Institute of Mathematical Sciences, C.I.T. Campus, Taramani Chennai 600113, India
Email:
dsn@imsc.ernet.in
Received by editor(s):
February 1, 2001
Published electronically:
April 24, 2001
Communicated by:
Frances C. Kirwan
Article copyright:
© Copyright 2001
American Mathematical Society
