Monomialization of Morphisms from 3-folds to Surfaces / Steven Dale Cutkosky

Date :

Type : Livre / Book

Langue / Language : anglais / English

ISBN : 978-3-540-48030-3

Morphismes (mathématiques)

Variétés algébriques

Variétés à 3 dimensions

Surfaces algébriques

Mathématiques

Géométrie algébrique

Classification Dewey : 510

Classification Dewey : 516.35

Collection : Lecture notes in mathematics / Heidelberg : Springer , 2001-

Relation : Monomialization of morphisms from 3-folds to surfaces / Steven Dale Cutkosky / Berlin : Springer

Résumé / Abstract : 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.