On the rationality of $SU(r,d)$

David C. Butler

On the rationality of $SU(r,d)$

alg-geom 2008-02-03 v2 Algebraic Geometry

Authors: David C. Butler

Abstract

Let SU(r,d) be the moduli space of rank r, degree d vector bundles over a smooth projective curve of genus $g\ge 2$ . If (r,d)=1 and d divides r+1, then SU is rational. Furthermore, if $0<\delta < r$ and all prime divisors of $\delta$ divide r, and if d divides $r-\delta$ , then SU is rational. The proof is a variation on a result of Newstead and modifications due to Ballico and then Boden and Yokogawa.

Keywords

moduli space vector bundle rationality smooth projective curve SU(r,d)

Cite

@article{arxiv.alg-geom/9705008,
  title  = {On the rationality of $SU(r,d)$},
  author = {David C. Butler},
  journal= {arXiv preprint arXiv:alg-geom/9705008},
  year   = {2008}
}

Comments

24 pages, AMS-TeX, corrected proof of Proposition 3

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