Geometry Over Nonclosed Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry Over Nonclosed Fields write by Fedor Bogomolov. This book was released on 2017-02-09. Geometry Over Nonclosed Fields available in PDF, EPUB and Kindle. Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.
Aspects of Algebraic Geometry Over Non Algebraically Closed Fields
Aspects of Algebraic Geometry Over Non Algebraically Closed Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Aspects of Algebraic Geometry Over Non Algebraically Closed Fields write by Tomas Sander. This book was released on 1996. Aspects of Algebraic Geometry Over Non Algebraically Closed Fields available in PDF, EPUB and Kindle.
Birational Geometry, Rational Curves, and Arithmetic
Birational Geometry, Rational Curves, and Arithmetic - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Birational Geometry, Rational Curves, and Arithmetic write by Fedor Bogomolov. This book was released on 2013-05-17. Birational Geometry, Rational Curves, and Arithmetic available in PDF, EPUB and Kindle. This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.
Nonarchimedean and Tropical Geometry
Nonarchimedean and Tropical Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonarchimedean and Tropical Geometry write by Matthew Baker. This book was released on 2016-08-18. Nonarchimedean and Tropical Geometry available in PDF, EPUB and Kindle. This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.
Geometry of Higher Dimensional Algebraic Varieties
Geometry of Higher Dimensional Algebraic Varieties - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry of Higher Dimensional Algebraic Varieties write by Yoichi Miyaoka. This book was released on 1997. Geometry of Higher Dimensional Algebraic Varieties available in PDF, EPUB and Kindle. The subject of this book is the classification theory and geometry of higher dimensional varieties: existence and geometry of rational curves via characteristic p-methods, manifolds with negative Kodaira dimension, vanishing theorems, theory of extremal rays (Mori theory), and minimal models. The book gives a state-of-the-art introduction to a difficult and not readily accessible subject which has undergone enormous development in the last two decades. With no loss of precision, the volume focuses on the spread of ideas rather than on a deliberate inclusion of all proofs. The methods presented vary from complex analysis to complex algebraic geometry and algebraic geometry over fields of positive characteristics. The intended audience includes students in algebraic geometry and analysis as well as researchers in these fields and experts from other areas who wish to gain an overview of the theory.
