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Algebraic Geometry I: Schemes: With Examples and Exercises by Ulrich Goertz, ...

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eBay item number:326118213254
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Item specifics

Condition
New: A new, unread, unused book in perfect condition with no missing or damaged pages. See the ...
ISBN
9783658307325
Publication Name
Algebraic Geometry I: Schemes: with Examples and Exercises
Publisher
Springer Spektrum
Subject
Mathematics
Publication Year
2020
Series
Springer Studium Mathematik-Master
Type
Textbook
Format
Paperback
Language
English
Item Height
244 mm
Author
Ulrich Goertz, Torsten Wedhorn
Item Weight
998 g
Item Width
170 mm
Number of Pages
626 Pages

About this product

Product Information

Algebraic geometry has its origin in the study of systems of polynomial equations f (x, . . ., x )=0, 1 1 n . . . f (x, . . ., x )=0. r 1 n Here the f ? k[X, . . ., X ] are polynomials in n variables with coe?cients in a ?eld k. i 1 n n ThesetofsolutionsisasubsetV(f, . . ., f)ofk . Polynomialequationsareomnipresent 1 r inandoutsidemathematics, andhavebeenstudiedsinceantiquity. Thefocusofalgebraic geometry is studying the geometric structure of their solution sets. n If the polynomials f are linear, then V(f, . . ., f ) is a subvector space of k. Its i 1 r size is measured by its dimension and it can be described as the kernel of the linear n r map k ? k, x=(x, . . ., x ) ? (f (x), . . ., f (x)). 1 n 1 r For arbitrary polynomials, V(f, . . ., f ) is in general not a subvector space. To study 1 r it, one uses the close connection of geometry and algebra which is a key property of algebraic geometry, and whose ?rst manifestation is the following: If g = g f +. . . g f 1 1 r r is a linear combination of the f (with coe?cients g ? k[T, . . ., T ]), then we have i i 1 n V(f, . . ., f)= V(g, f, . . ., f ). Thus the set of solutions depends only on the ideal 1 r 1 r a? k[T, . . ., T ] generated by the f .

Product Identifiers

Publisher
Springer Spektrum
ISBN-13
9783658307325
eBay Product ID (ePID)
21046664473

Product Key Features

Number of Pages
626 Pages
Language
English
Publication Name
Algebraic Geometry I: Schemes: with Examples and Exercises
Publication Year
2020
Subject
Mathematics
Type
Textbook
Author
Ulrich Goertz, Torsten Wedhorn
Series
Springer Studium Mathematik-Master
Format
Paperback

Dimensions

Item Height
244 mm
Item Weight
998 g
Item Width
170 mm

Additional Product Features

Country/Region of Manufacture
Germany
Title_Author
Torsten Wedhorn, Ulrich Goertz

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