On the Rationality of Certain Strata of the Lange Stratification of Stable Vector Bundles on Curves
نویسنده
چکیده
Let X be a smooth projective curve of genus g ≥ 2 and S(r, d) the moduli scheme of all rank r stable vector bundles of degree d on X. Fix an integer k with 0 < k < r. H. Lange introduced a natural stratification of S(r, d) using the degree of a rank k subbundle of any E ∈ S(r, d) with maximal degree. Every non-dense stratum, say W (k, r − k, a, d − a), has in a natural way a fiber structure h : W (k, r−k, a, d−a) → Pic(X)×Pic(X) with h dominant. Here we study the rationality or the unirationality of the generic fiber of h. 2000 Mathematics Subject Classification: 14H60.
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