Algebra, Arithmetic and Geometry with Applications: Papers from Shreeram S. Abhyankar’s 70th Birthday Conference

777 Pages·2004·19.49 MB·English

by  Chris Christensen

(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:2)(cid:7)(cid:11)(cid:12)(cid:13)(cid:14)(cid:5)(cid:12)(cid:11)(cid:15)(cid:10)(cid:8)(cid:16)(cid:17)(cid:10)(cid:18)(cid:5)(cid:19)(cid:14)(cid:5)(cid:12)(cid:7)(cid:20)
(cid:21)(cid:11)(cid:12)(cid:13)(cid:10)(cid:2)(cid:22)(cid:22)(cid:3)(cid:11)(cid:15)(cid:8)(cid:12)(cid:11)(cid:19)(cid:16)(cid:23)
Springer-Verlag Berlin Heidelberg GmbH
C. Christensen • G. Sundaram· A. Sathaye· C. Bajaj
(Editors)
Algebra, Arithmetic
and Geometry
with Applications
Papers from Shreeram S. Abhyankar's
70th Birthday Conference
, Springer
Editors:
Chris Christensen Ganesh Sundaram
Northern Kentucky University Bell Labs
Department of Mathematics 67, Whippany Road
and Computer Science Whippany, NJ 07981, USA
Highland Heights, KY 41099, USA e-mail: [email protected]
e-mail: [email protected]
Avinash Sathaye Chandrajit Bajaj
University of Kentucky Department of Computer Sciences
Department of Mathematics University of Texas at Austin
Lexington, KY 40506, USA Austin, TX, 78712, USA
e-mail: [email protected] e-mail: [email protected]
Library of Congress CataIoging·in-Publication Data
Algebra, aritlunetic, and geometry, witb applications : papers ftom Shreerarn S.
Abhyankar's 70tb birtbday conference / C. Christensen, G. Sundaram, A. Satbaye (editors).
p. ClJL
lncludes bibliographical references and index.
ISBN 978-3-540-00475-2 ISBN 978-3-642-18487-1 (eBook)
DOI 10.1007/978-3-642-18487-1
l. Algebra--Congresses. 2. Geometry-Congresses. 3. Aritlunetic-Congresses. I.
Abhyankar, Shreeram Sbankar. Il. Christensen, C. (Chris), 1946-III. Sundaram, G.
(Ganesh), 1965-IV. Satbaye, A. M. (Avinash Madhav), 1948-
QA150.A4172003
512--dc21
2003054376
Mathematics Subject Classification (2000) 14-06, 12-06, 13-06
ISBN 978-3-540-00475-2
This work is subjectto copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically
the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any
otherway, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions
ofthe German Copyright I.aw ofSeptember 9, 1965, in its current version, and permission for use must always be obtained
from Springer-Verlag. Violations are liable for prosecution under the German Copyright I.aw.
springeronline.com
© Springer-Verlag Berlin Heidelberg 2004
OriginaIly published by Springer-Verlag Berlin Heidelberg New York in 2004
The use of general descriptive names, registered names, trademarks etc. in this publication does not imply, even in the
absence of a specific statement, that such names are exempt from the relevant protective laws and regnlations and
therefore free for general use.
Cover design: Erich Kirchner, Heidelberg
Typesetting: I.e-TeX Jelonek, Schmidt & Vockler GbR, I.eipzig
Printed on acid-free paper 46/3142ck-5 4 3 21 O
Withelders watchingover and mothers looking after,
joinedwitha new son; our days were full of joy!
Shreeramand Yvonne Abhyankar, Lafayette 1970
Inspiredby Bhavabhati's verse describing sentiments ofRania
Contents
Preface
C. Christensen and G.S. Sundaram ............................... 1
A Robust, Computationally Efficient Methodology
to Set Service Levels for Components
in Assemble-to-Order Environments
H.S. Abhyankar................................................. 15
Smale Strategies for Prisoner’s Dilemma Type Games
K. Abhyankar .................................................. 45
Remembrances of Prof. Shreeram S. Abhyankar
and ABC of Singularities
Shreedhar S. Abhyankar.......................................... 49
Thoughts on Symplectic Groups and Symplectic Equations
Shreeram S. Abhyankar and N.F.J. Inglis .......................... 63
Field Generators for the Quantum Plane
J. Alev and F. Dumas ........................................... 127
Bounding Singular Surfaces of General Type
V. Alexeev and S. Mori .......................................... 143
Toric Modifications of Free Toric Varieties
A. Assi and M. Barile ........................................... 175
Recent Remarks on Analytical Equivalence
A. de Azevedo .................................................. 183
Behavior of the Torsion of the Differential Module
of an Algebroid Curve Under Quadratic Transformations
R.W. Berger ................................................... 189
Note on Equisingularity in Codimension 1
and Characteristic p (cid:2)= 0
I. Bermejo ..................................................... 203
VIII Contents
Toric Structure of the Graded Algebra
Relative to a Valuation
A. Campillo and C. Galindo...................................... 219
Postulation of Adjoint Ideals and Geometry
of Projective Curves
N. Chiarli, S. Greco and R. Notari................................ 235
Belghitti-Gruson or Semple?
V. Cossart ..................................................... 259
2S4 ∗Q8-extensions
T. Crespo...................................................... 263
The Structure of Morphisms
S.D. Cutkosky .................................................. 273
Around the Abhyankar-Moh Theorem
A. van den Essen ............................................... 283
PSL2(11) is Admissible for all Number Fields
W. Feit........................................................ 295
Adjoints and Max Noether’s Fundamentalsatz
W. Fulton...................................................... 301
Continuity Loci for Polynomial Systems
A. Galligo and M. Kwiecin´ski .................................... 315
Asymptotically Optimal Towers of Curves over Finite Fields
E.-U. Gekeler .................................................. 325
The Hilbert Series of Pfaffian Rings
S.R. Ghorpade and C. Krattenthaler............................... 337
The Impact of the Infinite Primes on the Riemann
Hypothesis for Characteristic p Valued L-series
D. Goss ....................................................... 357
General Elements of Complete Ideals and Valuations
Centered at a Two-dimensional Regular Local Ring
S. Greco and K. Kiyek........................................... 381
Exceptional Polynomials over Arbitrary Fields
R. Guralnick and J. Saxl......................................... 457
Abhyankar’s Local Conjecture on Fundamental Groups
D. Harbater and K.F. Stevenson .................................. 473
Contents IX
Questions of Connectedness of the Hilbert Scheme of Curves
in P3
R. Hartshorne .................................................. 487
Catenary Local Rings
with Geometrically Normal Formal Fibers
W. Heinzer, C. Rotthaus and S. Wiegand .......................... 497
Diamond Closure
M. Hochster and J.D. V´elez ...................................... 511
A Determinantal Formula for the Hilbert Series
of One-sided Ladder Determinantal Rings
C. Krattenthaler and M. Rubey ................................... 525
Multiplicities of Singular Points in Schubert Varieties
of Grassmannians
V. Kreiman and V. Lakshmibai ................................... 553
Geometric Applications of the Residue Theorem
on Algebraic Curves
E. Kunz ....................................................... 565
On p-Groups in Characteristic p
A. Ledet ....................................................... 591
Degree Two Generalized Iteration of q-Additive Polynomials
P.A. Loomis.................................................... 601
Wild Singularites on the Fermat Curve over Z
H. Maeda ...................................................... 609
Algebraic Curves over F3 with Many Rational Points
I. Luengo and B. Lo´pez.......................................... 619
Gro¨bner Bases of Symmetric Quotients and Applications
R.I. Michler.................................................... 627
Abstract Embeddings of Concrete Matrix-Groups
S.B. Mulay..................................................... 639
Some Generalization of Melville Theorem
K.N. Ponomarev................................................ 667
Multiple Planes Ramified over One-place Curves
P. Russell...................................................... 673
An Application of Generalized Newton Puiseux Expansions
A. Sathaye ..................................................... 687
X Contents
Elliptic Subfields and Automorphisms
of Genus 2 Function Fields
T. Shaska and H. V¨olklein ....................................... 703
Some Ideas in the Classification of the Finite Simple Groups
G. Stroth ...................................................... 725
Abhyankar’s Nice Equations
G.S. Sundaram ................................................. 733
The Scientific WorkPlace Computational Interface
Steven L. Swanson .............................................. 745
Diophantine Approximation in Finite Characteristic
D.S. Thakur.................................................... 757
Puiseux Expansions in Nonzero Characteristic
S. Vaidya ...................................................... 767
Arithmetical-Geometrical Galois Representations
and the Inverse Galois Problem
N. Vila ........................................................ 775
Polynomials and Power Series
Shreeram S. Abhyankar .......................................... 783
Author Index................................................. 785
List of Contributors
Hari S. Abhyankar Jacques Alev
DIGITAS Prudential Towers Universit´e de Reims
800 Boylston Street Laboratoire de Math´ematiques
Boston, MA 02199, USA C.N.R.S. U.M.R. 6056, B.P. 1039
[email protected] 51687 Reims Cedex 2, France
[email protected]
Kashi Abhyankar
Valery Alexeev
University of California
Department of Mathematics
Berkeley, CA, USA
University of Georgia
Current address:
Athens, GA 30605, USA
Kashi Abhyankar Behrstock
[email protected]
Morgan Stanley
1585 Broadway
New York, NY 10036, USA Abdallah Assi
kashi.abhyankar@ Universit´e d’Angers
morganstanley.edu D´epartement de Math´ematiques
2 bd Lavoisier
49045 Angers Cedex 01, France
Shreedhar S. Abhyankar [email protected]
Holkar Science College Indore
Current address:
Alberto de Azevedo
Flat No. 8B
Universidade de Bras´ılia
AMRISH
Departamento de Matematica
Survey No. 115
Bras´ılia DF 70910-900, Brazil
Shivateerth Nagar (off Paud Road)
[email protected]
Pune 411 038, India
[email protected]
Margherita Barile
Universita` degli Studi di Bari
Shreeram S. Abhyankar Dipartimento Interuniversitario di
Mathematics Department Matematica
Purdue University Via E. Orabona 4
West Lafayette, IN 47907, USA 70125 Bari, Italia
[email protected] [email protected]