國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Complex analytic desingularization

Aroca, Jose Manuel.

Complex analytic desingularization

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Complex analytic desingularizationby Jose Manuel Aroca, Heisuke Hironaka, Jose Luis Vicente.
作者:	Aroca, Jose Manuel.
其他作者:	Hironaka, Heisuke.
出版者:	Tokyo :Springer Japan :2018.
面頁冊數:	xxix, 330 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Geometry, Algebraic.
電子資源:	https://doi.org/10.1007/978-4-431-49822-3
ISBN:	9784431498223$q(electronic bk.)

Complex analytic desingularization
Aroca, Jose Manuel.

Complex analytic desingularization[electronic resource] /by Jose Manuel Aroca, Heisuke Hironaka, Jose Luis Vicente. - Tokyo :Springer Japan :2018. - xxix, 330 p. :ill., digital ;24 cm.

Prologue -- 1 Complex-Analytic Spaces and Elements -- 2 The Weierstrass Preparation Theorem and Its Consequences -- 3 Maximal Contact -- 4 Groves and Polygroves -- 5 The Induction Process -- Epilogue: Singularities of differential equations -- Bibliography -- Index.

[From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near "worst" singular points of a complex analytic space obtained by successive "permissible" blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka's ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry. In addition, the book contains an elegant presentation of all the prerequisites of complex analytic geometry, including basic definitions and theorems needed to follow the development of ideas and proofs. Its epilogue presents the use of similar ideas in the resolution of singularities of complex analytic foliations. This text will be particularly useful and interesting for readers of the younger generation who wish to understand one of the most fundamental results in algebraic and analytic geometry and invent possible extensions and applications of the methods created to prove it.

ISBN: 9784431498223$q(electronic bk.)

Standard No.: 10.1007/978-4-431-49822-3doiSubjects--Topical Terms:

190843
Geometry, Algebraic.

LC Class. No.: QA564 / .A763 1998

Dewey Class. No.: 516.35

Complex analytic desingularization
LDR:03346nmm a2200325 a 4500 001 545849
003 DE-He213
005 20190326154039.0
006 m d
007 cr nn 008maaau
008 190530s2018 ja s 0 eng d
020 $a 9784431498223$q(electronic bk.)
020 $a 9784431702184$q(paper)
024 7 $a 10.1007/978-4-431-49822-3 $2 doi
035 $a 978-4-431-49822-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA564 $b .A763 1998
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
090 $a QA564 $b .A769 1998
100 1 $a Aroca, Jose Manuel. $3 824945
245 1 0 $a Complex analytic desingularization $h [electronic resource] / $c by Jose Manuel Aroca, Heisuke Hironaka, Jose Luis Vicente.
260 $a Tokyo : $b Springer Japan : $b Imprint: Springer, $c 2018.
300 $a xxix, 330 p. : $b ill., digital ; $c 24 cm.
505 0 $a Prologue -- 1 Complex-Analytic Spaces and Elements -- 2 The Weierstrass Preparation Theorem and Its Consequences -- 3 Maximal Contact -- 4 Groves and Polygroves -- 5 The Induction Process -- Epilogue: Singularities of differential equations -- Bibliography -- Index.
520 $a [From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near "worst" singular points of a complex analytic space obtained by successive "permissible" blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka's ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry. In addition, the book contains an elegant presentation of all the prerequisites of complex analytic geometry, including basic definitions and theorems needed to follow the development of ideas and proofs. Its epilogue presents the use of similar ideas in the resolution of singularities of complex analytic foliations. This text will be particularly useful and interesting for readers of the younger generation who wish to understand one of the most fundamental results in algebraic and analytic geometry and invent possible extensions and applications of the methods created to prove it.
650 0 $a Geometry, Algebraic. $3 190843
650 0 $a Singularities (Mathematics) $3 185806
650 1 4 $a Algebraic Geometry. $3 274807
700 1 $a Hironaka, Heisuke. $3 824946
700 1 $a Vicente, Jose Luis. $3 824947
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-4-431-49822-3
950 $a Mathematics and Statistics (Springer-11649)