TL;DR
This paper derives a formula for the fundamental cycle of the limit subscheme of effective Cartier divisors in degenerating algebraic families, expressing it as a sum of Cartier divisors on the components.
Contribution
It provides a new explicit formula for the fundamental cycle of limit subschemes in degenerating families of algebraic varieties.
Findings
Formula for the fundamental cycle of limit subschemes
Expresses cycle as a sum of Cartier divisors on components
Applicable to degenerations to reducible varieties
Abstract
Consider a one-parameter family of algebraic varieties degenerating to a reducible one. Our main result is a formula for the fundamental cycle of the limit subscheme of any family of effective Cartier divisors. The formula expresses this cycle as a sum of Cartier divisors, not necessarily effective, of the components of the limit variety.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation