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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Counting divisors with prescribed singularities


Author: Israel Vainsencher
Journal: Trans. Amer. Math. Soc. 267 (1981), 399-422
MSC: Primary 14N10
MathSciNet review: 626480
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Abstract: Given a family of divisors $ \{ {D_s}\} $ in a family of smooth varieties $ \{ {Y_s}\} $ and a sequence of integers $ {m_1}, \ldots ,{m_t}$, we study the scheme parametrizing the points $ (s,{y_1}, \ldots ,{y_t})$ such that $ {y_i}$ is a (possibly infinitely near) $ {m_i}$-fold point of $ {D_s}$. We obtain a general formula which yields, as special cases, the formula of de Jonquières and other classical results of Enumerative Geometry. We also study the questions of finiteness and the multiplicities of the solutions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0626480-7
PII: S 0002-9947(1981)0626480-7
Keywords: Projective algebraic variety, families of divisors, multiple points, scheme of zeros, locally free sheaves, Chern classes, contact conditions
Article copyright: © Copyright 1981 American Mathematical Society