An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
Schlichenmaier, Martin.
An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces [electronic resource] / by Martin Schlichenmaier. - XIII, 149 p. online resource. - Lecture Notes in Physics, 322 0075-8450 ; . - Lecture Notes in Physics, 322 .
from a physicist's viewpoint -- Manifolds -- Topology of riemann surfaces -- Analytic structure -- Differentials and integration -- Tori and jacobians -- Projective varieties -- Moduli space of curves -- Vector bundles, sheaves and cohomology -- The theorem of riemann-roch for line bundles -- The mumford isomorphism on the moduli space.
This lecture is intended as an introduction to the mathematical concepts of algebraic and analytic geometry. It is addressed primarily to theoretical physicists, in particular those working in string theories. The author gives a very clear exposition of the main theorems, introducing the necessary concepts by lucid examples, and shows how to work with the methods of algebraic geometry. As an example he presents the Krichever-Novikov construction of algebras of Virasaro type. The book will be welcomed by many researchers as an overview of an important branch of mathematics, a collection of useful formulae and an excellent guide to the more extensive mathematical literature.
9783540459347
10.1007/BFb0113492 doi
Geometry, algebraic.
Quantum theory.
Algebraic topology.
Algebraic Geometry.
Theoretical, Mathematical and Computational Physics.
Elementary Particles, Quantum Field Theory.
Algebraic Topology.
QA564-609
516.35
An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces [electronic resource] / by Martin Schlichenmaier. - XIII, 149 p. online resource. - Lecture Notes in Physics, 322 0075-8450 ; . - Lecture Notes in Physics, 322 .
from a physicist's viewpoint -- Manifolds -- Topology of riemann surfaces -- Analytic structure -- Differentials and integration -- Tori and jacobians -- Projective varieties -- Moduli space of curves -- Vector bundles, sheaves and cohomology -- The theorem of riemann-roch for line bundles -- The mumford isomorphism on the moduli space.
This lecture is intended as an introduction to the mathematical concepts of algebraic and analytic geometry. It is addressed primarily to theoretical physicists, in particular those working in string theories. The author gives a very clear exposition of the main theorems, introducing the necessary concepts by lucid examples, and shows how to work with the methods of algebraic geometry. As an example he presents the Krichever-Novikov construction of algebras of Virasaro type. The book will be welcomed by many researchers as an overview of an important branch of mathematics, a collection of useful formulae and an excellent guide to the more extensive mathematical literature.
9783540459347
10.1007/BFb0113492 doi
Geometry, algebraic.
Quantum theory.
Algebraic topology.
Algebraic Geometry.
Theoretical, Mathematical and Computational Physics.
Elementary Particles, Quantum Field Theory.
Algebraic Topology.
QA564-609
516.35