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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Counting divisors with prescribed singularities
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by Israel Vainsencher PDF
Trans. Amer. Math. Soc. 267 (1981), 399-422 Request permission

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
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 267 (1981), 399-422
  • MSC: Primary 14N10
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0626480-7
  • MathSciNet review: 626480