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.

中文翻译：

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对数余切丛、Chern-Mather 类和 Huh-Sturmfels 对合猜想

利用对数余切丛中的紧化，我们获得了在具有正常交叉补的开放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任意非常仿射簇的 Chern-Mather 类的几何描述，概括了 Huh 的早期结果，该结果在平滑和 schön 假设下成立。作为第二个应用，我们证明了 Huh 和 Sturmfels 在 2013 年猜想的与截面最大似然（ML）度和 ML 二度相关的对合公式。