Monomialization of Morphisms from 3-Folds to Surfaces

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Monomialization of Morphisms from 3-Folds to Surfaces

Steven D. Cutkosky, "Monomialization of Morphisms from 3-Folds to Surfaces"
2002 | pages: 240 | ISBN: 3540437800 | PDF | 1,5 mb

A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S.
The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.

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Tags: Monomialization, Morphisms, Surfaces

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