论文标题
全球光彩 - 关于赫维兹空间的无理论
Global Brill--Noether Theory over the Hurwitz Space
论文作者
论文摘要
令$ c $为$ g $属的曲线。代数曲线理论中的一个基本问题是要了解指定度$ d $的地图$ c \ to \ mathbb {p}^r $。当$ c $是一般的时候，这种地图的模量空间就被Brill的主要定理所理解，而不是理论。尽管在过去的三十年中进行了大量研究，但对于固定高态的曲线而言，同样完整的图片被证明是难以捉摸的。在这里，我们通过证明Brill的所有主要定理的类似物（在这种情况下）的理论来完成这样的图片。作为推论，我们证明了Eisenbud和Schreyer的猜想，内容涉及$ \ Mathbb {p}^1 $上的向量捆绑包的广泛变形空间。
Let $C$ be a curve of genus $g$. A fundamental problem in the theory of algebraic curves is to understand maps $C \to \mathbb{P}^r$ of specified degree $d$. When $C$ is general, the moduli space of such maps is well-understood by the main theorems of Brill--Noether theory. Despite much study over the past three decades, a similarly complete picture has proved elusive for curves of fixed gonality. Here we complete such a picture, by proving analogs of all of the main theorems of Brill--Noether theory in this setting. As a corollary, we prove a conjecture of Eisenbud and Schreyer regarding versal deformation spaces of vector bundles on $\mathbb{P}^1$.
