Sequences of multiple products and cohomology classes for foliations of complex curves
A. Zuevsky
TL;DR
This paper develops a cohomology theory for complex curve foliations using transversality in multiple product sequences of rational functions, providing explicit formulas for invariants.
Contribution
It introduces a novel cohomology framework based on transversality conditions for sequences of products related to vertex algebra cohomology.
Findings
Explicit formulas for cohomology invariants
New transversality conditions for product sequences
Application to codimension one foliations
Abstract
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex curves. Explicit formulas for cohomology invariants results from consideration transversality conditions applied to sequences of multiple products for elements of chain-cochain transversal complexes defined for codimension one foliations.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Commutative Algebra and Its Applications