Monomialization of Morphisms from 3-Folds to Surfaces

Monomialization of Morphisms from 3-Folds to Surfaces

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English | 248 pages | Springer (August 6, 2002) | 3540437800 | PDF | 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.