1980
DOI: 10.1090/s0002-9947-1980-0576865-1
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On a simplicial complex associated to the monodromy

Abstract: Abstract.Suppose we have a complex analytic family, Vr \t\ < 1, such that the generic fibre is a nonsingular complex manifold of complex dimension n. Let T denote the monodromy induced from going once around the singular fibre and let / denote the identity map. We shall associate to the singular fibre a simplicial complex T, which is at most n-dimensional. Then under certain conditions on the family V, (which are satisfied for the Milnor fibration of an isolated singularity or if the V, are compact Kahler), th… Show more

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Cited by 6 publications
(5 citation statements)
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“…This requires the introduction of a simplicial set which encodes the intersections of the various components of D, and which we call the Clemens complex. Such a simplicial set has been used by Clemens in [14] in his study of the Picard-Lefschetz transformation (see also [23]). 3.1.1.…”
Section: Clemens Complexes and Variantsmentioning
confidence: 99%
“…This requires the introduction of a simplicial set which encodes the intersections of the various components of D, and which we call the Clemens complex. Such a simplicial set has been used by Clemens in [14] in his study of the Picard-Lefschetz transformation (see also [23]). 3.1.1.…”
Section: Clemens Complexes and Variantsmentioning
confidence: 99%
“…is...ip = ∅. This complex was first introduced by G. L. Gordon to study monodromy in analytic families [9], and whose homotopy type has been more recently studied by D. A. Stepanov in the setting where D is the exceptional divisor of a resolution of an isolated singularity [16], [17], [18], and by A. Thuillier in a more general setting [19].…”
Section: The Dual Complex Of a Simple Normal Crossings Divisor Let D =mentioning
confidence: 99%
“…Just think of the prime components D i as the vertices, non-empty 2-fold intersections D i ∩ D j as the edges, non-empty 3-fold intersections D i ∩ D j ∩ D k as the 2-faces, and so on. This simplicial complex, first studied by G. L. Gordon [9], is absent of any algebrao-geometric structure yet carries with it important skeletal information.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…gives a more complicated example (see [3]). If we blow up the origin, the exceptional divisor E ′ | X ′ consists of 3 lines E i , i = 1, 2, 3; every 2 of them intersect at a single point.…”
Section: Some Remarksmentioning
confidence: 99%