Milnor fiber boundary of a non-isolated surface singularity
著者
書誌事項
Milnor fiber boundary of a non-isolated surface singularity
(Lecture notes in mathematics, 2037)
Springer, c2012
大学図書館所蔵 全47件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 231-236) and index
内容説明・目次
内容説明
In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.
目次
- 1 Introduction.- 2 The topology of a hypersurface germ f in three variables Milnor fiber.- 3 The topology of a pair (f
- g).- 4 Plumbing graphs and oriented plumbed 3-manifolds.- 5 Cyclic coverings of graphs.- 6 The graph GC of a pair (f
- g). The definition.- 7 The graph GC . Properties.- 8 Examples. Homogeneous singularities.- 9 Examples. Families associated with plane curve singularities.- 10 The Main Algorithm.- 11 Proof of the Main Algorithm.- 12 The Collapsing Main Algorithm.- 13 Vertical/horizontal monodromies.- 14 The algebraic monodromy of H1( F). Starting point.- 15 The ranks of H1( F) and H1( F nVg) via plumbing.- 16 The characteristic polynomial of F via P# and P#.- 18 The mixed Hodge structure of H1( F).- 19 Homogeneous singularities.- 20 Cylinders of plane curve singularities: f = f 0(x
- y).- 21 Germs f of type z f 0(x
- y).- 22 The T
- -family.- 23 Germs f of type ~ f (xayb
- z). Suspensions.- 24 Peculiar structures on F. Topics for future research.- 25 List of examples.- 26 List of notations
「Nielsen BookData」 より