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An Invitation to Quantum Cohomology Kontsevich's Formula for Rational Plane Curv
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Item specifics
- Condition
- ISBN
- 9780817644567
About this product
Product Identifiers
Publisher
Birkhäuser Boston
ISBN-10
0817644563
ISBN-13
9780817644567
eBay Product ID (ePID)
50224051
Product Key Features
Number of Pages
Xiv, 162 Pages
Publication Name
Invitation to Quantum Cohomology : Kontsevich's Formula for RATIONAL Plane Curves
Language
English
Publication Year
2006
Subject
Physics / Quantum Theory, Algebra / Abstract, Topology, Physics / Mathematical & Computational, Geometry / Algebraic
Type
Textbook
Subject Area
Mathematics, Science
Series
Progress in Mathematics Ser.
Format
Hardcover
Dimensions
Item Height
0.2 in
Item Weight
33.5 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2006-924437
TitleLeading
An
Reviews
"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, "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, "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
Dewey Edition
22
Series Volume Number
249
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
516.3/5
Table Of Content
Prologue: Warming Up with Cross Ratios, and the Definition of Moduli Space.- Stable n-pointed Curves.- Stable Maps.- Enumerative Geometry via Stable Maps.- Gromov--Witten Invariants.- Quantum Cohomology.
Synopsis
This elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves; the viewpoint is mostly that of enumerative geometry. 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. 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, geometers, and physicists working in the field., This 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. Kontsevich's formula is initially established in the framework of classical enumerative geometry, then as a statement about reconstruction for Gromov?Witten invariants, and finally, using generating functions, as a special case of the associativity of the quantum product. 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., This elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves; the viewpoint of mostly that of enumerative geometry. 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. 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, geometers, and physicists working in the field., This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology. A striking demonstration of the potential of these techniques is provided by Kont- vich's famous formula, which solves a long-standing question: How many plane rational curves of degree d pass through 3d -- 1 given points in general position? The formula expresses the number of curves for a given degree in terms of the numbers for lower degrees. A single initial datum is required for the recursion, namely, the case d = I, which simply amounts to the fact that through two points there is but one line. Assuming the existence of the Kontsevich spaces of stable maps and a few of their basic properties, we present a complete proof of the formula, and use the formula as a red thread in our Invitation to Quantum Cohomology. For more information about the mathematical content, see the Introduction. The canonical reference for this topic is the already classical Notes on Stable Maps and Quantum Cohomology by Fulton and Pandharipande 29], cited henceforth as FP-NOTES. We have traded greater generality for the sake of introducing some simplifications. We have also chosen not to include the technical details of the construction of the moduli space, favoring the exposition with many examples and heuristic discussions., This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology. A striking demonstration of the potential of these techniques is provided by Kont- vich's famous formula, which solves a long-standing question: How many plane rational curves of degree d pass through 3d -- 1 given points in general position? The formula expresses the number of curves for a given degree in terms of the numbers for lower degrees. A single initial datum is required for the recursion, namely, the case d = I, which simply amounts to the fact that through two points there is but one line. Assuming the existence of the Kontsevich spaces of stable maps and a few of their basic properties, we present a complete proof of the formula, and use the formula as a red thread in our Invitation to Quantum Cohomology. For more information about the mathematical content, see the Introduction. The canonical reference for this topic is the already classical Notes on Stable Maps and Quantum Cohomology by Fulton and Pandharipande [29], cited henceforth as FP-NOTES. We have traded greater generality for the sake of introducing some simplifications. We have also chosen not to include the technical details of the construction of the moduli space, favoring the exposition with many examples and heuristic discussions.
LC Classification Number
QA564-609
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- s***h (297)- Feedback left by buyer.Past 6 monthsVerified purchase100+ year old book, in excellent condition and exactly as described. Excellent transaction. Shiping was immediate and received 4 days after ordering. Packaging was first rate. I highly recommend this seller and will do business again.hYoung Americans in Japan Edward Greey Jewett Family Oto Nambo Vintage 1899 hc (#226303767901)
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- 1***s (95)- Feedback left by buyer.Past yearVerified purchaseThis is a very nice seller to do business with. Item looked just as described, even better than it looked. All questions were answered quickly, Item was reasonably priced and so was the shipping. The magazine was wrapped very well. I would recommend this seller, and I will be purchasing from again very soon.Nutshell News for complete miniatures hobbyist Magazine October 1990 dollhouse (#226653221325)