Cohomological Blowups of Graded Artinian Gorenstein Algebras along Surjective Maps
Cohomological Blowups of Graded Artinian Gorenstein Algebras along Surjective Maps
复制标题
分级 Artinian Gorenstein 代数沿满射映射的上同调放大
DOI：
10.1093/imrn/rnac002
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发表时间：
2022
影响因子：
1
通讯作者：
Watanabe, Junzo
中科院分区：
文献类型：
--
作者：
Iarrobino, Anthony;Macias Marques, Pedro;McDaniel, Chris;Seceleanu, Alexandra;Watanabe, Junzo
引入了分次Artin Gorenstein代数沿着满射的上同调爆破，简称BUG（blowupGorenstein）.这是为了把一个射影流形沿着一个射影子流形的爆破的上同调环转换到代数的上下文中。我们表明，除其他事项外，一个BUG是一个连接的总和，它是一般纤维在一个平坦的家庭代数，它保留了强大的莱夫谢茨财产。我们还表明，标准的分级压缩代数很少BUG，我们分类这些BUG是完整的交叉。我们在这份手稿中包括了许多例子。
We introduce the cohomological blowup of a graded Artinian Gorenstein algebra along a surjective map, which we term BUG (blowup Gorenstein) for short. This is intended to translate to an algebraic context the cohomology ring of a blowup of a projective manifold along a projective submanifold. We show, among other things, that a BUG is a connected sum, that it is the general fiber in a flat family of algebras, and that it preserves the strong Lefschetz property. We also show that standard graded compressed algebras are rarely BUGs, and we classify those BUGs that are complete intersections. We have included many examples throughout this manuscript.