Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces
Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces
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K3 表面上的最小分辨率、Chow 形式和 Ulrich 丛
DOI：
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发表时间：
2012
期刊：
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通讯作者：
A. Ortega
中科院分区：
文献类型：
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作者：
M. Aprodu;G. Farkas;A. Ortega
射影簇X上点的最小分辨猜想（MRC）预言X中一般点集的Betti数与X的几何（希尔伯特函数）所允许的一样小。在很大程度上，我们解决了这个猜想的曲线C具有一般的模。我们证明了，独立于亏格，MRC对C上的d度和维数为r的一般线性系统成立当且仅当d> 2 r-1。然后，我们继续寻找一个完整的解决方案的理想生成猜想的曲线与一般模。在另一个方向上，我们证明了K3曲面允许每个秩的Ulrich丛。我们应用它来描述K3曲面的Chow形式的普法夫方程。
The Minimal Resolution Conjecture (MRC) for points on a projective variety X predicts that the Betti numbers of general sets of points in X are as small as the geometry (Hilbert function) of X allows. To a large extent, we settle this conjecture for a curve C with general moduli. We show that, independently of the genus, MRC holds for a general linear system of degree d and dimension r on C if and only if d>2r-1. We then proceed to find a full solution to the Ideal Generation Conjecture for curves with general moduli. In a different direction, we prove that K3 surfaces admit Ulrich bundles of every rank. We apply this to describe a pfaffian equation for the Chow form of a K3 surface.