论文标题
Koszul模块具有消失的代数几何共振
Koszul modules with vanishing resonance in algebraic geometry
论文作者
论文摘要
我们讨论了在矢量空间的第二个楔形产品中与子空间相关的有限长度Koszul模块的分级组件的均匀消失结果的各种应用。以前，有限长度的Koszul模块已用于证明Green在通用规范曲线的共同体上的猜想。现在，我们将代数品种增厚的共同体有效稳定，在曲线模量空间上的分隔线，K3表面上的曲线列出曲线的几何形状以及偏斜成对的脱落二层化位点。我们还表明，曲线上足够积极的等级2向量束的稳定性受共振的控制。
We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace in the second wedge product of a vector space. Previously Koszul modules of finite length have been used to give a proof of Green's Conjecture on syzygies of generic canonical curves. We now give applications to effective stabilization of cohomology of thickenings of algebraic varieties, divisors on moduli spaces of curves, enumerative geometry of curves on K3 surfaces and to skew-symmetric degeneracy loci. We also show that the stability of sufficiently positive rank 2 vector bundles on curves is governed by resonance.
