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- W36842783 abstract "Let f: X → Y be a map. Its set of r-fold points is $$begin{array}{*{20}{c}} {{{text{M}}_{{text{r}}}}{text{ = }}{ {text{x}}varepsilon {text{X|}}} & {{text{there}} {text{exist}}} & {{{text{x}}_{2}},...,{{text{x}}_{{text{r}}}}} & {{text{with}}} & {{text{f(}}{{text{x}}_{{text{i}}}}){text{ = f}}({text{x}})} ;} end{array}$$the xi must be distinct from x and from each other, but they may lie “infinitely close” (that is, determine tangent directions along the fiber f-1f(x)). An r-fold-point formula is a polynomial expression in the invariants of f which gives, under appropriate hypotheses, the number of r-fold points, weighted by natural multiplicities, or the class mr of a natural positive cycle supported by Mr. The theory of these formulas will be surveyed here, concentrating on some of the author’s recent work, Kleiman [1981b], [1982]. Aside from a few comments, the setting will be algebraic geometry, although the formulas and their proofs have a universal character." @default.
- W36842783 created "2016-06-24" @default.
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- W36842783 date "1982-01-01" @default.
- W36842783 modified "2023-09-25" @default.
- W36842783 title "Multiple Point Formulas for Maps" @default.
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- W36842783 doi "https://doi.org/10.1007/978-1-4684-6726-0_11" @default.
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