论文标题
属属的几何形状
Geometry of genus one fine compactified universal Jacobians
论文作者
论文摘要
我们引入了一个普通的抽象概念，即用于任意属的淋巴结曲线的精细压缩雅各布。 我们专注于属1，并在单个节点曲线和通用家族的情况下，在稳定尖曲线的模量空间内证明了精细压缩的雅各布人的组合分类结果。我们表明，如果可以将属1的淋巴结曲线的精细压缩的雅各布扩展到曲线的平滑状态，则可以将其描述为相对于某些极化的稳定滑轮的模量空间。在普遍的情况下，我们构建了1属的新示例，即属于普遍的雅各布人。然后，我们给出了每个属1的hodge和betti数字的公式。
We introduce a general abstract notion of fine compactified Jacobian for nodal curves of arbitrary genus. We focus on genus 1 and prove combinatorial classification results for fine compactified Jacobians in the case of a single nodal curve and in the case of the universal family over the moduli space of stable pointed curves. We show that if the fine compactified Jacobian of a nodal curve of genus 1 can be extended to a smoothing of the curve, then it can be described as the moduli space of stable sheaves with respect to some polarisation. In the universal case we construct new examples of genus 1 fine compactified universal Jacobians. Then we give a formula for the Hodge and Betti numbers of each genus 1 fine compactified universal Jacobian and prove that their even cohomology is algebraic.
