LEADER 03957nam 2200613Ia 450 001 9910132668203321 005 20200520144314.0 010 $a9783642236471 010 $a3642236472 024 7 $a10.1007/978-3-642-23647-1 035 $a(CKB)3390000000021959 035 $a(SSID)ssj0000610279 035 $a(PQKBManifestationID)11387613 035 $a(PQKBTitleCode)TC0000610279 035 $a(PQKBWorkID)10624489 035 $a(PQKB)10073678 035 $a(DE-He213)978-3-642-23647-1 035 $a(MiAaPQ)EBC3070537 035 $a(PPN)159084695 035 $a(EXLCZ)993390000000021959 100 $a20120119d2012 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMilnor fiber boundary of a non-isolated surface singularity /$fAndras Nemethi, Agnes Szilard 205 $a1st ed. 2012. 210 $aHeidelberg ;$aNew York $cSpringer$dc2012 215 $a1 online resource (XII, 240 p.) 225 1 $aLecture notes in mathematics,$x0075-8434 ;$v2037 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642236464 311 08$a3642236464 320 $aIncludes bibliographical references (p. 231-236) and index. 327 $a1 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. 330 $aIn the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2037. 606 $aTopology 606 $aMilnor fibration 606 $aSingularities (Mathematics) 615 0$aTopology. 615 0$aMilnor fibration. 615 0$aSingularities (Mathematics) 676 $a514 700 $aNemethi$b Andras$00 701 $aSzilard$b Agnes$0515211 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910132668203321 996 $aMilnor fiber boundary of a non-isolated surface singularity$9855920 997 $aUNINA