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arXiv · 2112.11247

On proper intersections on a singular analytic space

Mats Andersson·Håkan Samuelsson Kalm
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Abstract

Given a reduced analytic space $Y$ we introduce a class of {\it nice} cycles, including all effective $\mathbb{Q}$-Cartier divisors. Equidimensional nice cycles that intersect properly allow for a natural intersection product. Using $\bar{\partial}$-potentials and residue calculus we provide an intrinsic way of defining this product. The intrinsic definition makes it possible to prove global formulas. In case $Y$ is smooth all cycles are differences of nice cycles, and so we get a new way to define classical proper intersections.

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Mats Andersson, Håkan Samuelsson Kalm. 2021-12-21. On proper intersections on a singular analytic space. https://arxiv.org/abs/2112.11247

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