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.
Lecture Notes in Mathematics Editors: J.–M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
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Steven Dale Cutkosky
Monomialization of Morphisms from 3-Folds to Surfaces
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Author Steven Dale Cutkosky Department of Mathematics University of Missouri Columbia MO 65211 U.S.A. e-mail:
[email protected] http://www.math.missouri.edu/˜cutkosky
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Cutkosky, Steven Dale: Monomialization of morphisms from 3-folds to surfaces / Steven Dale Cutkosky. - Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Lecture notes in mathematics ; 1786) ISBN 3-540-43780-0
Mathematics Subject Classification (2000): 14E15, 14D06 ISSN 0075-8434 ISBN 3-540-43780-0 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf