Listing 1 - 10 of 21 | << page >> |
Sort by
|
Choose an application
This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.
Algebraic geometry. --- Algebraic Geometry. --- Geometry, Enumerative. --- Logarithms. --- Tropical geometry. --- Geometria enumerativa --- Geometria tropical --- Logaritmes
Choose an application
Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.
Number theory. --- Algebraic geometry. --- Number Theory. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of --- Algebra --- Arakelov theory. --- Arakelov geometry --- Arithmetical algebraic geometry --- Geometria algebraica --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes
Choose an application
The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.
Algebraic geometry. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Geometry, Algebraic. --- Geometria algebraica --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes
Choose an application
This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems. The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology. This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.
Geometry. --- Projective geometry. --- Algebra. --- Projective Geometry. --- Mathematics --- Mathematical analysis --- Projective geometry --- Geometry, Modern --- Euclid's Elements --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Geometria algebraica --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes
Choose an application
Geometria algebraica --- Punts racionals (Geometria) --- Geometria algebraica aritmètica --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes --- Geometry, Algebraic. --- Rational points (Geometry) --- Mathematics --- Points, Rational (Geometry) --- Arithmetical algebraic geometry --- Algebraic geometry --- Geometry
Choose an application
Transcendental functions --- Geometry, Algebraic --- Functions, Transcendental --- Functions, Special --- Funcions transcendents --- Geometria algebraica --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes --- Funcions especials --- Funcions de Bessel --- Funcions gamma --- Funcions hipergeomètriques --- Funcions theta
Choose an application
Geometria algebraica --- Àlgebra commutativa --- Geometry, Algebraic. --- Commutative algebra. --- Algebra. --- Algebraic geometry --- Geometry --- Algebra --- Mathematics --- Mathematical analysis --- Àlgebres commutatives --- Àlgebra --- Teoria de la dimensió (Àlgebra) --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes
Choose an application
Geometria algebraica --- Representacions d'àlgebres --- Àlgebra --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes --- Geometria algèbrica --- Geometry, Algebraic. --- Representations of algebras. --- Algebra --- Algebraic geometry --- Geometry
Choose an application
Geometry, Algebraic. --- Representations of algebras. --- Algebra --- Algebraic geometry --- Geometry --- Geometria algebraica --- Representacions d'àlgebres --- Àlgebra --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes
Choose an application
Curves, Algebraic. --- Corbes algebraiques --- Geometria algebraica --- Algebraic curves --- Algebraic varieties --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Funcions abelianes --- Corbes algèbriques --- Corbes el·líptiques --- Corbes modulars --- Corbes quàrtiques
Listing 1 - 10 of 21 | << page >> |
Sort by
|