The Albanese mapping for a punctual Hilbert scheme. I. Irreducibility of the fibers
Author:
Mark E. Huibregtse
Journal:
Trans. Amer. Math. Soc. 251 (1979), 267-285
MSC:
Primary 14C05; Secondary 14E99, 14K99
DOI:
https://doi.org/10.1090/S0002-9947-1979-0531979-9
MathSciNet review:
531979
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be the canonical mapping from an algebraic surface X to its Albanese variety A,
the n-fold symmetric product of X, and
the punctual Hilbert scheme parameterizing 0-dimensional closed subschemes of length n on X. The latter is a nonsingular and irreducible variety of dimension
, and the ``Hilbert-Chow'' morphism
is a birational map which desingularizes
.
This paper studies the composite morphism








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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1979-0531979-9
Keywords:
Punctual Hilbert scheme,
symmetric product,
Albanese variety,
Albanese mapping,
algebraic surface
Article copyright:
© Copyright 1979
American Mathematical Society