東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

An undergraduate primer in algebraic...

Ciliberto, Ciro.

FindBook

Google Book

Amazon

博客來

An undergraduate primer in algebraic geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An undergraduate primer in algebraic geometry/ by Ciro Ciliberto.
作者:	Ciliberto, Ciro.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	xi, 327 p. :ill., digital ;24 cm.
內容註:	1 Affine and projective algebraic sets -- 2 Basic notions of elimination theory and applications -- 3 Zariski closed subsets and ideals in the polynomials ring -- 4 Some topological properties -- 5 Regular and rational functions -- 6 Morphisms -- 7 Rational maps -- 8 Product of varieties -- 9 More on elimination theory -- 10 Finite morphisms -- 11 Dimension -- 12 The Cayley form -- 13 Grassmannians -- 14 Smooth and singular points -- 15 Power series -- 16 A ne plane curves -- 17 Projective plane curves -- 18 Resolution of singularities of curves -- 19 Divisors, linear equivalence, linear series -- 20 The Riemann-Roch Theorem.
Contained By:	Springer Nature eBook
標題:	Geometry, Algebraic. -
電子資源:	https://doi.org/10.1007/978-3-030-71021-7
ISBN:	9783030710217

An undergraduate primer in algebraic geometry
Ciliberto, Ciro.

An undergraduate primer in algebraic geometry[electronic resource] /by Ciro Ciliberto. - Cham :Springer International Publishing :2021. - xi, 327 p. :ill., digital ;24 cm. - Unitext ;v.129. - Unitext ;v.129..

1 Affine and projective algebraic sets -- 2 Basic notions of elimination theory and applications -- 3 Zariski closed subsets and ideals in the polynomials ring -- 4 Some topological properties -- 5 Regular and rational functions -- 6 Morphisms -- 7 Rational maps -- 8 Product of varieties -- 9 More on elimination theory -- 10 Finite morphisms -- 11 Dimension -- 12 The Cayley form -- 13 Grassmannians -- 14 Smooth and singular points -- 15 Power series -- 16 A ne plane curves -- 17 Projective plane curves -- 18 Resolution of singularities of curves -- 19 Divisors, linear equivalence, linear series -- 20 The Riemann-Roch Theorem.

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.

ISBN: 9783030710217

Standard No.: 10.1007/978-3-030-71021-7doiSubjects--Topical Terms:

532048
Geometry, Algebraic.

LC Class. No.: QA564 / .C555 2021

Dewey Class. No.: 516.35

An undergraduate primer in algebraic geometry
LDR:02923nmm a2200337 a 4500 001 2240102
003 DE-He213
005 20210730110404.0
006 m d
007 cr nn 008maaau
008 211111s2021 sz s 0 eng d
020 $a 9783030710217 $q (electronic bk.)
020 $a 9783030710200 $q (paper)
024 7 $a 10.1007/978-3-030-71021-7 $2 doi
035 $a 978-3-030-71021-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA564 $b .C555 2021
072 7 $a PBM $2 bicssc
072 7 $a MAT012000 $2 bisacsh
072 7 $a PBM $2 thema
082 0 4 $a 516.35 $2 23
090 $a QA564 $b .C572 2021
100 1 $a Ciliberto, Ciro. $3 901306
245 1 3 $a An undergraduate primer in algebraic geometry $h [electronic resource] / $c by Ciro Ciliberto.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xi, 327 p. : $b ill., digital ; $c 24 cm.
490 1 $a Unitext ; $v v.129
505 0 $a 1 Affine and projective algebraic sets -- 2 Basic notions of elimination theory and applications -- 3 Zariski closed subsets and ideals in the polynomials ring -- 4 Some topological properties -- 5 Regular and rational functions -- 6 Morphisms -- 7 Rational maps -- 8 Product of varieties -- 9 More on elimination theory -- 10 Finite morphisms -- 11 Dimension -- 12 The Cayley form -- 13 Grassmannians -- 14 Smooth and singular points -- 15 Power series -- 16 A ne plane curves -- 17 Projective plane curves -- 18 Resolution of singularities of curves -- 19 Divisors, linear equivalence, linear series -- 20 The Riemann-Roch Theorem.
520 $a 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.
650 0 $a Geometry, Algebraic. $3 532048
650 1 4 $a Geometry. $3 517251
650 2 4 $a Projective Geometry. $3 2056109
650 2 4 $a Algebra. $3 516203
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Unitext ; $v v.129. $3 3494773
856 4 0 $u https://doi.org/10.1007/978-3-030-71021-7
950 $a Mathematics and Statistics (SpringerNature-11649)