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

Format:

Book

Author/Creator:

Cutkosky, Steven Dale, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1786.

Lecture Notes in Mathematics, 0075-8434 ; 1786

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebraic Geometry.

Local Subjects:

Algebraic Geometry.

Physical Description:

1 online resource (VIII, 240 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.

System Details:

text file PDF

Summary:

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.

Contents:

1. Introduction

2. Local Monomialization

3. Monomialization of Morphisms in Low Dimensions

4. An Overview of the Proof of Monomialization of Morphisms from 3 Folds to Surfaces

5. Notations

6. The Invariant v

7. The Invariant v under Quadratic Transforms

8. Permissible Monoidal Transforms Centered at Curves

9. Power Series in 2 Variables

10. Ar(X)

11.Reduction of v in a Special Case

12. Reduction of v in a Second Special Case

13. Resolution 1

14. Resolution 2

15. Resolution 3

16. Resolution 4

17. Proof of the main Theorem

18. Monomialization

19. Toroidalization

20. Glossary of Notations and definitions

References.

Other Format:

Printed edition:

ISBN:

9783540480303

Access Restriction:

Restricted for use by site license.