Generic initial ideal theory for coordinate rings of flag varieties [PhD thesis] PDF
Preview Generic initial ideal theory for coordinate rings of flag varieties [PhD thesis]
INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road. Ann Arbor. Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9510332 Generic initial ideal theory for coordinate rings of flag varieties Rippel, Christoph Johann, Ph.D. University of California, Los Angeles, 1994 U M I 300 N. Zeeb Rd. Ann Arbor, MI 48106 UNIVERSITY OF CALIFORNIA Los Angeles Generic Initial Ideal Theory for Coordinate Rings of Flag Varieties A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Mathematics by Christoph Johann Rippel 1994 The dissertation tif Christoph Johann Rippel is approved. A . ^ David A. Gieseker Vik U T ji Robert K. Lazarsfeld 1M/1A/ Hidenori Sonoda Mark L. Green, Committee Chair University of California, Los Angeles 1994 ii DEDICATION To Yuko and Andreas TABLE OF CONTENTS 0.1 Introduction................................................................................................... 1 0.2 Conventions................................................................................................... 3 0.3 Description of the individual sections..................................................... 4 1 Initial ideals...................................................................................................... 11 1.1 Tableaux ...................................................................................................... 11 1.2 A simplified straightening law .................................................................. 15 1.3 Quasi-monomial algebras and modules................................................. 23 1.4 Initial modules and initial specializations ........................................... 28 2 Generic initial ideals................................................................................... 38 2.1 Introduction to infinitesimal tableaux calculations ........................... 38 2.2 Generic initial ideals.................................................................................. 43 2.3 More on ideals of generic type................................................................. 48 2.4 Saturation of generic initial ideals........................................................... 52 Bibliography......................................................................................................... 61 iv ACKNOWLEDGMENTS I would like to thank the Department of Mathematics and UCLA for their fi nancial support during my graduate studies. I would like thank David Gieseker and Robert Lazarsfeld for their support and encouragement, Alfonso Tortora for many interesting conversations, and Greg Kallo and Shelly Cook for their help in preparing this document. I am very grateful to my advisor Mark Green whose help and patience made this thesis possible. I owe him much. v VITA December 19, 1962 Born, Kaiserslautern, Germany 1989 Diplom in Mathematik Universitat Kaiserslautern 1989-1994 Teaching Assistant-Associate-Fellow and Research Assistant University of California, Los Angeles 1991 Candidate of Philosophy in Mathematics University of California, Los Angeles
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