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