The Art Of Doing Algebraic Geometry

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The Art Of Doing Algebraic Geometry

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Author : Thomas Dedieu
language : en
Publisher: Springer Nature
Release Date : 2023-04-14

The Art Of Doing Algebraic Geometry written by Thomas Dedieu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-14 with Mathematics categories.

This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.

Current Developments In Algebraic Geometry

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Author : Lucia Caporaso
language : en
Publisher: Cambridge University Press
Release Date : 2012-03-19

Current Developments In Algebraic Geometry written by Lucia Caporaso and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-19 with Mathematics categories.

This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.

Arithmetic Algebraic Geometry

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Author : G., van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Arithmetic Algebraic Geometry written by G., van der Geer 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.

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.

Advances In Algebraic Geometry Motivated By Physics

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Author : Emma Previato
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Advances In Algebraic Geometry Motivated By Physics written by Emma Previato 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 2001 with Mathematics categories.

Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, ``Enumerative Geometry in Physics,'' held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend. The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.

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.

Algorithmic And Experimental Methods In Algebra Geometry And Number Theory

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Author : Gebhard Böckle
language : en
Publisher: Springer
Release Date : 2018-03-22

Algorithmic And Experimental Methods In Algebra Geometry And Number Theory written by Gebhard Böckle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-22 with Mathematics categories.

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Perspectives On Four Decades Of Algebraic Geometry Volume 2

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Author : Alberto Albano
language : en
Publisher: Birkhäuser
Release Date : 2024-10-13

Perspectives On Four Decades Of Algebraic Geometry Volume 2 written by Alberto Albano and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-13 with Mathematics categories.

The second of a two-part volume, this collection offers a unifying vision of algebraic geometry, exploring its evolution over the last four decades as well as state-of-the art research. With chapters written by established leaders in the field as well as younger researchers, readers will gain a wide-ranging perspective of the area. The volume also commemorates the significant talent and contributions of Alberto Collino, whose scientific accomplishments helped shape the themes and topics covered. Perspectives on Four Decades of Algebraic Geometry, Volume 2 will be a valuable resource for those interested in the ways algebraic geometry has expanded over the years and continues to grow.

Homotopy Theory And Arithmetic Geometry Motivic And Diophantine Aspects

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Author : Frank Neumann
language : en
Publisher: Springer Nature
Release Date : 2021-09-29

Homotopy Theory And Arithmetic Geometry Motivic And Diophantine Aspects written by Frank Neumann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-29 with Mathematics categories.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.

Arithmetic Algebraic Geometry

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Author : Jean-Louis Colliot-Thelene
language : en
Publisher: Springer
Release Date : 2006-11-15

Arithmetic Algebraic Geometry written by Jean-Louis Colliot-Thelene and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

This volume contains three long lecture series by J.L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their topics are respectively the connection between algebraic K-theory and the torsion algebraic cycles on an algebraic variety, a new approach to Iwasawa theory for Hasse-Weil L-function, and the applications of arithemetic geometry to Diophantine approximation. They contain many new results at a very advanced level, but also surveys of the state of the art on the subject with complete, detailed profs and a lot of background. Hence they can be useful to readers with very different background and experience. CONTENTS: J.L. Colliot-Thelene: Cycles algebriques de torsion et K-theorie algebrique.- K. Kato: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.- P. Vojta: Applications of arithmetic algebraic geometry to diophantine approximations.

Arithmetic And Geometry Of K3 Surfaces And Calabi Yau Threefolds

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Author : Radu Laza
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-12

Arithmetic And Geometry Of K3 Surfaces And Calabi Yau Threefolds written by Radu Laza 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 2013-06-12 with Mathematics categories.

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.