Monomialization of Morphisms from 3 Folds to Surfaces
Edition: 1 edition
Publisher: Springer
Published: September 24, 2002
Language: eng
Format: Paperback
Number of pages: 235
ISBN-13: 9783540437802
Subjects: Algebraic Geometry; Linear algebra; Surfaces, Algebraic; Image Processing (Engineering); Threefolds (Algebraic geometry; Technology; Mathematics; Science/Mathematics; Optics; Algebra - Linear; General; Geometry - Algebraic; Algebraic Variety; Mathematics / Algebra / Linear; Mathematics / Geometry / Algebraic; Mathematics-Geometry - Algebraic; Medical-General; Monomialization; Morphism; Resolution of Singularities; Threefolds (Algebraic geometry); Algebraic varieties; Geometry - Differential; Morphisms (Mathematics)
Description: 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.