论文标题
盖塔（Gaeta
Gaeta resolutions and strange duality over rational surfaces
论文作者
论文摘要
在投影平面和大多数两步的海泽布鲁克表面爆炸，那里有强烈的特殊线条束序列，我们获得了有关这些线束相干滑轮的Gaeta分辨率的基础结果。在适当的条件下，我们显示了可半固定滑轮的座位，不承认Gaeta决议至少具有2个。然后，我们研究了Le Potier的奇怪二元猜想。在这些表面上，对于两个正交数值类别，一个等级有一个排名一个，另一个具有足够的正面Chern类，我们表明这种奇怪的形态是具有侵入性的。证明的主要步骤是使用Gaeta决议来证明某些相关的引号计划是有限的，并减少了，从而可以使用作者的先前论文来枚举它们。
Over the projective plane and at most two-step blowups of Hirzebruch surfaces, where there are strong full exceptional sequences of line bundles, we obtain foundational results about Gaeta resolutions of coherent sheaves by these line bundles. Under appropriate conditions, we show the locus of semistable sheaves not admitting Gaeta resolutions has codimension at least 2. We then study Le Potier's strange duality conjecture. Over these surfaces, for two orthogonal numerical classes where one has rank one and the other has sufficiently positive first Chern class, we show that the strange morphism is injective. The main step in the proof is to use Gaeta resolutions to show that certain relevant Quot schemes are finite and reduced, allowing them to be enumerated using the authors' previous paper.
