Fourier Functor and its Application to the Moduli of Bundles on an Abelian Variety
Fourier Functor and its Application to the Moduli of Bundles on an Abelian Variety
复制标题
傅里叶函子及其在阿贝尔簇上丛模的应用
DOI：
--
复制
发表时间：
1987
期刊：
影响因子：
--
通讯作者：
S. Mukai
中科院分区：
文献类型：
--
作者：
S. Mukai
在研讨会上，我们讨论了K3曲面上的矢量束及其在K3曲面几何中的应用。我们演讲的大部分内容都包含在《论K3曲面上束的模空间》这篇论文中，该论文出现在1984年塔塔研究所矢量束研讨会的论文集中。在本文中，我们将讨论阿贝尔变体上的向量束。在[12]中，我们定义了傅里叶函子并展示了它的基本性质。这个函子是研究阿贝尔变体上的向量束（或者更一般地说是相干束）的有力工具，正如我们在[12]中对皮卡德束所展示的那样。在本文中，推广[12]中的结果，我们将证明一个束及其傅里叶变换具有相同的局部（在Zariski拓扑中）模空间，并将其应用于阿贝尔变体X上向量束的模空间的研究。在第1节中，我们将证明当X是属：：2:3的超椭圆曲线的雅可比变体时，Picard束的模空间是不约简的。在剩下的部分中，我们将主要研究u型捆，这是第一次在b[20]在阿贝尔面上进行研究。
At the symposium we talked on the vector bundles on a K3 surface and applications to the geometry of a K3 surface. Most content of our talk is contained in the paper "On the moduli space of bundles on K3 surfaces, I" to appear in the proceeding of the symposium on vector bundles at Tata Institute in 1984. In this article we discuss the vector bundles on an abelian variety instead. In [12], we have defined the Fourier functor and shown its basic properties. This functor is a powerful tool for investigating the vector bundle (or coherent sheaves, more generally) on an abelian variety as we have shown for the Picard bundles in [12]. In this article, generalizing the results in [12], we shall show that a sheaf and its Fourier transform have the same local (in the Zariski topology) moduli space and apply this to the study of the moduli space of vector bundles on an abelian variety X. In Section 1, we shall show that the moduli space of the Picard bundles is non-reduced in the case X is the Jacobian variety of a hyperelliptic curve of genus::2:3. In the remaining sections, we shall mainly study the sheaves Of U-type, which were first studied in [20] over an abelian surface.