对数余切束，chen - mather类，和Huh-Sturmfels对合猜想

IF 3.1 1区数学 Q1 MATHEMATICS Communications on Pure and Applied Mathematics Pub Date : 2023-09-15 DOI:10.1002/cpa.22156

Laurenţiu G. Maxim, Jose Israel Rodriguez, Botong Wang, Lei Wu

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引用次数: 3

摘要

利用对数余切束中的紧化，我们得到了具有正交补的开嵌入下拉格朗日循环推进的Chern类的公式。这概括了Aluffi和Wu-Zhou的早期结果。我们的公式的第一个应用是对任意非常仿射变化的chen - mather类的几何描述，推广了Huh在光滑和schön假设下的早期结果。作为第二种应用，我们证明了一个由Huh和Sturmfels在2013年推测的关于截面最大似然度(ML)和ML二度的对合公式。

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Logarithmic cotangent bundles, Chern-Mather classes, and the Huh-Sturmfels involution conjecture

Using compactifications in the logarithmic cotangent bundle, we obtain a formula for the Chern classes of the pushforward of Lagrangian cycles under an open embedding with normal crossing complement. This generalizes earlier results of Aluffi and Wu-Zhou. The first application of our formula is a geometric description of Chern-Mather classes of an arbitrary very affine variety, generalizing earlier results of Huh which held under the smooth and schön assumptions. As the second application, we prove an involution formula relating sectional maximum likelihood (ML) degrees and ML bidegrees, which was conjectured by Huh and Sturmfels in 2013.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.