On the stability of the direct image of a generic vector bundle
On the stability of the direct image of a generic vector bundle
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发表时间：
2000
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通讯作者：
Arnaud Beauville
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作者：
Arnaud Beauville
我对这个猜想没有强烈的动机，除了它是一个相当自然的陈述。正如我们将在下面看到的，关键的情况是当L是线丛时；在[B]中使用当π是二重覆盖时的(容易)情况来控制X上的秩2向量丛的模空间上的theta因子。人们可能希望，对猜想的证明将导致对任意阶的theta线性系统的更好的理解。我们只得到了猜想方向的部分结果：我们将证明对于小阶子丛(§1)，对于χ的小值(L)(§2)，或者当π是étalle(§3)，稳定性是成立的。
I do not have a strong motivation towards the conjecture, except that it is a rather natural statement. As we will see below, the crucial case is when L is a line bundle; the (easy) case when π is a double covering was used in [B] to control the theta divisor on the moduli space of rank 2 vector bundles on X . One may hope that a proof of the conjecture would lead to a better understanding of the theta linear system in arbitrary rank. We have only partial results in the direction of the conjecture: we will show that stability holds with respect to sub-bundles of small degree ( § 1), for small values of χ(L) ( § 2), or when π is étale ( § 3).