02940nam 2200577 450 991078875800332120170918215821.01-4704-0136-3(CKB)3360000000464741(EBL)3113949(SSID)ssj0000889309(PQKBManifestationID)11497184(PQKBTitleCode)TC0000889309(PQKBWorkID)10876977(PQKB)11270550(MiAaPQ)EBC3113949(RPAM)4924619(PPN)19541439X(EXLCZ)99336000000046474120140909h19951995 uy 0engur|n|---|||||txtccrWeyl groups and birational transformations among minimal models /Kenji MatsukiProvidence, Rhode Island :American Mathematical Society,1995.©19951 online resource (146 p.)Memoirs of the American Mathematical Society,0065-9266 ;Number 557"July 1995, Volume 116, Number 557 (end of volume)."0-8218-0341-7 Includes bibliographical references.""Contents""; ""Chapter I. Introduction""; ""Chapter II. Weyl groups appearing in the symmetry among minimal models""; ""ÂII-1. 3â€?folds of general type â€? Weyl groups of finite type""; ""ÂII-1-1. The case of rational double points""; ""ÂII-1-2. The case of Del Pezzo surfaces""; ""ÂII-1-3. The case of ruled surfaces""; ""ÂII-2. Elliptic 3-folds â€? Weyl groups of affine type""; ""ÂII-2-1. The case of Kodairaâ€?type degenerations of elliptic curves""; ""ÂII-3. 3â€?folds with Kodaira dimension 1 â€? Weyl groups of hyperbolic type""""ÂII-3-1. The case of Picardâ€?Lefschetz reflections of K3 surfaces""""ÂII-4. 3-folds with Kodaira dimension 0""; ""ÂII-4-1. The case of generic quintic 3â€?folds""; ""Chapter III. Weyl groups for Fano 3â€?folds""; ""ÂIII-1. Characterization of the Weyl groups for Del Pezzo surfaces and its generalization to Fano manifolds of higher dimensions""; ""ÂIII-2. Flops in dimension 4""; ""ÂIII-3. Table for the Weyl groups for Fano 3â€?folds""; ""Chapter IV. Summary and speculation about the connection with algebraic groups""; ""References""Memoirs of the American Mathematical Society ;Number 557.Surfaces, AlgebraicWeyl groupsThreefolds (Algebraic geometry)Surfaces, Algebraic.Weyl groups.Threefolds (Algebraic geometry)516.3/5Matsuki Kenji1958-66401MiAaPQMiAaPQMiAaPQBOOK9910788758003321Weyl groups and birational transformations among minimal models3760001UNINA05142nam 22008415 450 991097456320332120250416110355.09786612964893978128296489112829648959781400837779140083777410.1515/9781400837779(CKB)2560000000049182(EBL)664559(OCoLC)705944534(SSID)ssj0000469101(PQKBManifestationID)12194618(PQKBTitleCode)TC0000469101(PQKBWorkID)10510513(PQKB)10137301(SSID)ssj0000543676(PQKBManifestationID)11354860(PQKBTitleCode)TC0000543676(PQKBWorkID)10530723(PQKB)10260622(DE-B1597)446841(OCoLC)1013946211(OCoLC)1029818777(OCoLC)1032685261(OCoLC)1037925500(OCoLC)1041989782(OCoLC)1046608148(OCoLC)1047020686(OCoLC)1049620159(OCoLC)1054880021(OCoLC)979749693(DE-B1597)9781400837779(MiAaPQ)EBC664559(Perlego)734995(FR-PaCSA)88957339(FRCYB88957339)88957339(EXLCZ)99256000000004918220190708d2008 fg engur|||||||||||txtccrFearless Symmetry Exposing the Hidden Patterns of Numbers - New Edition /Robert Gross, Avner AshNew edition with a New preface by the authorsPrinceton, NJ : Princeton University Press, [2008]©20081 online resource (307 p.)Description based upon print version of record.9780691138718 0691138710 Frontmatter -- Contents -- Foreword -- Preface To The Paperback Edition -- Preface -- Acknowledgments -- Greek Alphabet -- Part One. Algebraic Preliminaries -- Chapter 1. Representations -- Chapter 2. Groups -- Chapter 3. Permutations -- Chapter 4. Modular Arithmetic -- Chapter 5. Complex Numbers -- Chapter 6. Equations and Varieties -- Chapter 7. Quadratic Reciprocity -- Part Two. Galois Theory and Representations -- Chapter 8. Galois Theory -- Chapter 9. Elliptic Curves -- Chapter 10. Matrices -- Chapter 11. Groups of Matrices -- Chapter 12. Group Representations -- Chapter 13. The Galois Group Of A Polynomial -- Chapter 14. The Restriction Morphism -- Chapter 15. The Greeks Had a Name for it -- Chapter 16. Frobenius -- Part Three. Reciprocity Laws -- Chapter 17. Reciprocity Laws -- Chapter 18. One- And Two-Dimensional Representations -- Chapter 19. Quadratic Reciprocity Revisited -- Chapter 20. A Machine for Making Galois Representations -- Chapter 21. A Last Look at Reciprocity -- Chapter 22. Fermat's Last Theorem and Generalized Fermat Equations -- Chapter 23. Retrospect -- Bibliography -- IndexMathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two hundred years ago by French mathematician évariste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.Number theoryNumber theoryNumber theory.Number theory.512.7SK 180rvkAsh Avner, 1034316Gross Robert, DE-B1597DE-B1597BOOK9910974563203321Fearless Symmetry4359660UNINA