國立虎尾科技大學 |

An invitation to web geometry

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	An invitation to web geometry/ by Jorge Vitorio Pereira, Luc Pirio.
作者:	Pereira, Jorge Vitorio.
其他作者:	Pirio, Luc.
出版者:	Cham :Springer International Publishing : : 2015.,
面頁冊數:	xvii, 213 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Webs (Differential geometry) -
電子資源:	http://dx.doi.org/10.1007/978-3-319-14562-4
ISBN:	9783319145624 (electronic bk.)

An invitation to web geometry
Pereira, Jorge Vitorio.

An invitation to web geometry[electronic resource] /by Jorge Vitorio Pereira, Luc Pirio. - Cham :Springer International Publishing :2015. - xvii, 213 p. :ill., digital ;24 cm. - IMPA monographs ;v.2. - IMPA monographs ;v.2..

Local and Global Webs -- Abelian Relations -- Abel's Addition Theorem -- The Converse to Abel's Theorem -- Algebraization -- Exceptional Webs.

This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern's bound and Trepreau's algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.

ISBN: 9783319145624 (electronic bk.)

Standard No.: 10.1007/978-3-319-14562-4doiSubjects--Topical Terms:

1066708
Webs (Differential geometry)

LC Class. No.: QA648.5

Dewey Class. No.: 516.36

An invitation to web geometry
LDR:02079nam a2200325 a 4500 001 836514
003 DE-He213
005 20150922110008.0
006 m d
007 cr nn 008maaau
008 160421s2015 gw s 0 eng d
020 $a 9783319145624 (electronic bk.)
020 $a 9783319145617 (paper)
024 7 $a 10.1007/978-3-319-14562-4 $2 doi
035 $a 978-3-319-14562-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA648.5
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
082 0 4 $a 516.36 $2 23
090 $a QA648.5 $b .P436 2015
100 1 $a Pereira, Jorge Vitorio. $3 1066705
245 1 3 $a An invitation to web geometry $h [electronic resource] / $c by Jorge Vitorio Pereira, Luc Pirio.
260 $a Cham : $c 2015. $b Springer International Publishing : $b Imprint: Springer,
300 $a xvii, 213 p. : $b ill., digital ; $c 24 cm.
490 1 $a IMPA monographs ; $v v.2
505 0 $a Local and Global Webs -- Abelian Relations -- Abel's Addition Theorem -- The Converse to Abel's Theorem -- Algebraization -- Exceptional Webs.
520 $a This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern's bound and Trepreau's algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.
650 0 $a Webs (Differential geometry) $3 1066708
650 0 $a Geometry, Differential. $3 527830
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 672032
700 1 $a Pirio, Luc. $3 1066706
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a IMPA monographs ; $v v.2. $3 1066707
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-14562-4
950 $a Mathematics and Statistics (Springer-11649)