Limits of Cartier divisors

Details Limits of Cartier divisors Limits of Cartier divisors

2009-05-11

arxiv.org/abs/0905.1656v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

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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