Multigraded linear series and recollement
Multigraded linear series and recollement
复制标题
DOI：
10.1007/s00209-017-1965-1
复制
发表时间：
2017-01
影响因子：
0.8
通讯作者：
Alastair Craw;Yukari Ito;J. Karmazyn
中科院分区：
文献类型：
--
作者：
Alastair Craw;Yukari Ito;J. Karmazyn
给定一个具有全局生成向量丛集合的模式Y，研究了Y到Y上的自同态代数上的循环模的细模空间的泛态射。这将经典态射推广到无基点线丛的线性级数。我们描述了态射的图像，并提出了满射的充要条件，在一个模范畴的一个重元。当态射是满射时，这给出了图像的精细模空间解释，并且作为应用，我们表明，对于一个小的有限子群，每一个次最小的部分分辨率是同构的精细模空间，其中是定义重建代数的子代数E的被加数。我们还考虑应用Gorenstein仿射三倍，里德的配方揭示了一些光的代数类，从中可以重建一个给定的crepant决议。
Given a schemeYequipped with a collection of globally generated vector bundles, we study the universal morphism fromYto a fine moduli spaceof cyclic modules over the endomorphism algebra of. This generalises the classical morphism to the linear series of a basepoint-free line bundle on a scheme. We describe the image of the morphism and present necessary and sufficient conditions for surjectivity in terms of a recollement of a module category. When the morphism is surjective, this gives a fine moduli space interpretation of the image, and as an application we show that for a small, finite subgroup, every sub-minimal partial resolution ofis isomorphic to a fine moduli spacewhereis a summand of the bundleEdefining the reconstruction algebra. We also consider applications to Gorenstein affine threefolds, where Reid’s recipe sheds some light on the classes of algebra from which one can reconstruct a given crepant resolution.