Rationality Problem For Algebraic Tori
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Rationality Problem For Algebraic Tori
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Author : Akinari Hoshi
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-13
Rationality Problem For Algebraic Tori written by Akinari Hoshi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-13 with Affine algebraic groups categories.
The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank and is given. The authors show that there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension , and there exist exactly (resp. , resp. ) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension . The authors make a procedure to compute a flabby resolution of a -lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a -lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby -lattices of rank up to and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for -lattices holds when the rank , and fails when the rank is ...
Rationality Problems In Algebraic Geometry
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Author : Arnaud Beauville
language : en
Publisher: Springer
Release Date : 2016-12-06
Rationality Problems In Algebraic Geometry written by Arnaud Beauville and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-06 with Mathematics categories.
Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
Multiplicative Invariant Fields Of Dimension Leq 6
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Author : Akinari Hoshi
language : en
Publisher: American Mathematical Society
Release Date : 2023-03-09
Multiplicative Invariant Fields Of Dimension Leq 6 written by Akinari Hoshi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-09 with Mathematics categories.
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Encyclopaedia Of Mathematics
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Author : M. Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by M. Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Cohomological And Geometric Approaches To Rationality Problems
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Author : Fedor Bogomolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-03
Cohomological And Geometric Approaches To Rationality Problems written by Fedor Bogomolov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-03 with Mathematics categories.
Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
20 Lectures Delivered At The International Congress Of Mathematicians In Vancouver 1974
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1977-12-31
20 Lectures Delivered At The International Congress Of Mathematicians In Vancouver 1974 written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-12-31 with Mathematics categories.
Affine Algebraic Geometry
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Author : Kayo Masuda
language : en
Publisher: World Scientific
Release Date : 2013-05-20
Affine Algebraic Geometry written by Kayo Masuda and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-20 with Mathematics categories.
The present volume grew out of an international conference on affine algebraic geometry held in Osaka, Japan during 3–6 March 2011 and is dedicated to Professor Masayoshi Miyanishi on the occasion of his 70th birthday. It contains 16 refereed articles in the areas of affine algebraic geometry, commutative algebra and related fields, which have been the working fields of Professor Miyanishi for almost 50 years. Readers will be able to find recent trends in these areas too. The topics contain both algebraic and analytic, as well as both affine and projective, problems. All the results treated in this volume are new and original which subsequently will provide fresh research problems to explore. This volume is suitable for graduate students and researchers in these areas. Contents:Acyclic Curves and Group Actions on Affine Toric Surfaces (Ivan Arzhantsev and Mikhail Zaidenberg)Hirzeburch Surfaces and Compactifications of ℂ2 (M Furushima and A Ishida)Cyclic Multiple Planes, Branched Covers of Sn and a Result of D L Goldsmith (R V Gurjar)𝔸1*-Fibrations on Affine Threefolds (R V Gurjar, M Koras, K Masuda, M Miyanishi and P Russell)Miyanishi's Characterization of Singularities Appearing on 𝔸1-Fibrations Does Not Hold in Higher Dimensions (Takashi Kishimoto)A Galois Counterexample to Hilbert's Fourteenth Problem in Dimension Three with Rational Coefficients (Ei Kobayashi and Shigeru Kuroda)Open Algebraic Surfaces of Logarithmic Kodaira Dimension One (Hideo Kojima)Some Properties of ℂ* in ℂ2 (M Koras and P Russell)Abhyankar-Sathaye Embedding Conjecture for a Geometric Case (Tomoaki Ohta)Some Subgroups of the Cremona Groups (Vladimir L Popov)The Gonality of Singular Plane Curves II (Fumio Sakai)Examples of Non-Uniruled Surfaces with Pre-Tango Structures Involving Non-Closed Global Differential 1-Forms (Yoshifumi Takeda)Representations of 𝔾a of Codimension Two (Ryuji Tanimoto)The Projective Characterization of Genus Two Plane Curves Which Have One Place at Infinity (Keita Tono)Sextic Variety as Galois Closure Variety of Smooth Cubic (Hisao Yoshihara)Invariant Hypersurfaces of Endomorphisms of the Projective 3-Space (De-Qi Zhang) Readership: Graduate students and researchers in affine algebraic geometry. Keywords:Affine algebraic geometry;Commutative algebra;Polynomial algebra;Group actions;FibrationsKey Features:Many active researchers such as M Zaidenberg, R V Gurjar, M Koras, P Russell, F Sakai, V Popov, H Yoshihara, and D-Q Zhang contributed articles to this proceedingsMany viewpoints are taken into consideration to study surfaces and threefolds. These will give hints for further research in neighboring fields
Sobolev Besov And Triebel Lizorkin Spaces On Quantum Tori
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Author : Xiao Xiong
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-03-19
Sobolev Besov And Triebel Lizorkin Spaces On Quantum Tori written by Xiao Xiong and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with categories.
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative -torus (with a skew symmetric real -matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincaré type inequality for Sobolev spaces.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
European Congress Of Mathematics
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Author : Antal Balog
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
European Congress Of Mathematics written by Antal Balog and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the second volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua.