An Invitation to Quantum Cohomology: Kontsevich's Formula for Rational Plane Curves
BeschreibungThis book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational plane curves. Emphasis is given throughout the exposition to examples, heuristic discussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry.Some familiarity with basic algebraic geometry and elementary intersection theory is assumed. Each chapter concludes with some historical comments and an outline of key topics and themes as a guide for further study, followed by a collection of exercises that complement the material covered and reinforce computational skills. As such, the book is ideal for self-study, as a text for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory. The book will prove equally useful to graduate students in the classroom setting as to researchers in geometry and physics who wish to learn about the subject.
InhaltsverzeichnisPrologue: Warming Up with Cross Ratios, and the Definition of Moduli Space.
Stable n-pointed Curves.
Enumerative Geometry via Stable Maps.
Pressestimmen"The book seems to be ideally designed for a semester course or ambitious self-study." -Mathematical Reviews
"The book is intended to be a friendly introduction to quantum cohomology. It makes the reader acquainted with the notions of stable curves and stable maps, and their moduli spaces. These notions are central in the field. ... Each chapter ends with references for further readings, and also with a set of exercices which help fixing the ideas introduced in that chapter. This makes the book especially useful for graduate courses, and for graduate students who wish to learn about quantum cohomology." -Zentralblatt Math
"...The book is ideal for self-study, as a text for a mini-course in quantum cohomology, or a special topics text in a standard course in intersection theory. The book will prove equally useful to graduate students in the classroom setting as to researchers in geometry and physics who wish to learn about the subject" -Analele Stiintifice ale Universitatii "Al. I. Cuza" din Iasi
Untertitel: Kontsevich's Formula for Rational Plane Curves. 'Progress in Mathematics'. and and. Sprache: Englisch.
Verlag: SPRINGER VERLAG GMBH
Erscheinungsdatum: Oktober 2006
Seitenanzahl: 159 Seiten