Algebraic cobordism revisited
Algebraic cobordism revisited
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重温代数协边主义
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
R. Pandharipande
中科院分区：
文献类型：
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作者：
Marc Levine;R. Pandharipande
我们在代数几何中定义了一种基于双点奇点法交退化的余边理论。主要结果是重点余边理论与Levine和Morel以前定义的代数余边理论等价。双点协边理论提供了代数协边理论的一种简单的几何表示。作为推论，由射影空间的乘积给出的Lazard环有理地生成模为重点退化的所有非奇异射影簇.在相对的Donaldson-Thomas理论中，重点退化是自然产生的.我们用双点余边法证明了Donaldson-Thomas理论中的所有0次猜想：绝对猜想、相对猜想和等变猜想。
We define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities. The main result is the equivalence of double point cobordism to the theory of algebraic cobordism previously defined by Levine and Morel. Double point cobordism provides a simple, geometric presentation of algebraic cobordism theory. As a corollary, the Lazard ring given by products of projective spaces rationally generates all nonsingular projective varieties modulo double point degenerations.Double point degenerations arise naturally in relative Donaldson–Thomas theory. We use double point cobordism to prove all the degree 0 conjectures in Donaldson–Thomas theory: absolute, relative, and equivariant.