About G -bundles over elliptic curves

Yves Laszlo

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 2, page 413-424
  • ISSN: 0373-0956

Abstract

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Let G be a complex algebraic group, simple and simply connected, T a maximal torus and W the Weyl group. One shows that the coarse moduli space M G ( X ) parametrizing S -equivalence classes of semistable G -bundles over an elliptic curve X is isomorphic to [ Γ ( T ) ⊗ Z X ] / W . By a result of Looijenga, this shows that M G ( X ) is a weighted projective space.

How to cite

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Laszlo, Yves. "About $G$-bundles over elliptic curves." Annales de l'institut Fourier 48.2 (1998): 413-424. <http://eudml.org/doc/75287>.

@article{Laszlo1998,
abstract = {Let $G$ be a complex algebraic group, simple and simply connected, $T$ a maximal torus and $W$ the Weyl group. One shows that the coarse moduli space $M_G(X)$ parametrizing $S$-equivalence classes of semistable $G$-bundles over an elliptic curve $X$ is isomorphic to $[\Gamma (T)\otimes _\{\{\bf Z\}\} X]/W$. By a result of Looijenga, this shows that $M_G(X)$ is a weighted projective space.},
author = {Laszlo, Yves},
journal = {Annales de l'institut Fourier},
keywords = {semistable bundles; principal bundles over a complex elliptic curve; coarse moduli space},
language = {eng},
number = {2},
pages = {413-424},
publisher = {Association des Annales de l'Institut Fourier},
title = {About $G$-bundles over elliptic curves},
url = {http://eudml.org/doc/75287},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Laszlo, Yves
TI - About $G$-bundles over elliptic curves
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 2
SP - 413
EP - 424
AB - Let $G$ be a complex algebraic group, simple and simply connected, $T$ a maximal torus and $W$ the Weyl group. One shows that the coarse moduli space $M_G(X)$ parametrizing $S$-equivalence classes of semistable $G$-bundles over an elliptic curve $X$ is isomorphic to $[\Gamma (T)\otimes _{{\bf Z}} X]/W$. By a result of Looijenga, this shows that $M_G(X)$ is a weighted projective space.
LA - eng
KW - semistable bundles; principal bundles over a complex elliptic curve; coarse moduli space
UR - http://eudml.org/doc/75287
ER -

References

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  4. [BLS] A. BEAUVILLE, Y. LASZLO, C. SORGER, The Picard group of the moduli stack of G-bundles on a curve, preprint alg-geom/9608002, to appear in Compos. Math. Zbl0976.14024
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  10. [LS] Y. LASZLO, C. SORGERPicard group of the moduli stack of G-bundles, Ann. Scient. Éc. Norm. Sup., 4e série, 30 (1997), 499-525. 
  11. [LeP] J. LE POTIER, Fibrés vectoriels sur les courbes algébriques, Publ. Math. Univ. Paris 7, 35 (1995). Zbl0842.14025MR97c:14034
  12. [Lo] E. LOOIJENGA, Root systems and elliptic curves, Invent. Math., 38 (1976), 17-32. Zbl0358.17016MR57 #6015
  13. [Ra1] A. RAMANATHAN, Moduli for principal bundles over algebraic curves, I and II, Proc. Indian Acad. Sci. Math. Sci., 106 (1996), 301-328 and 421-449. Zbl0901.14007MR98b:14009a
  14. [Ra2] A. RAMANATHAN, Stable principal bundles on a compact Rieman surface, Math. Ann., 213 (1975), 129-152. Zbl0284.32019MR51 #5979
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  16. [T] L. TU, Semistable bundles over an elliptic curve, Adv. Math., 98 (1993), 1-26. Zbl0786.14021MR94a:14008

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