Limits of Cartier divisors
classification
🧮 math.AG
keywords
cartierdivisorscycleeffectivefamilyformulalimitalgebraic
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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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