Semistable reduction of a normal crossing \(\mathbb Q\)-divisor
type: Item
instance of: scholarly article
title: Semistable reduction of a normal crossing \(\mathbb Q\)-divisor
zbMATH Open document ID: 1357.32022
author: Jorge Martín-Morales
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2016-10-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1401.3926
review text: To simplify the combinatorics of an embedded resolution of a hypersurface singularity, the author introduced embedded \(\mathbb Q\)-resolutions. Here he shows that such a resolution can be used to determine the mixed Hodge structure on the cohomology of the Milnor fibre: basically the same construction as \textit{J. H. M. Steenbrink}'s original one [in: Real and compl. Singul., Proc. Nordic Summer Sch., Symp. Math., Oslo 1976, 525--563 (1977; Zbl 0373.14007)] via semi-stable reduction works. The paper concludes with some examples.
reviewed by: Jan Stevens
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 14D05
Mathematics Subject Classification ID: 32S45
Mathematics Subject Classification ID: 32S35
zbMATH DE Number: 6637358
zbMATH Keywords: monodromy
zbMATH Keywords: embedded \(\mathbb Q\)-resolution
zbMATH Keywords: semi-stable reduction
zbMATH Keywords: mixed Hodge structure
MaRDI profile type: Publication
OpenAlex ID: W2261028529
arXiv ID: 1401.3926
cites work: La fonction zeta d'une monodromie
cites work: Forme de Jordan de la monodromie des singularités superisolées de surfaces
cites work: Q3985696
cites work: Cartier and Weil divisors on varieties with quotient singularities
cites work: Intersection Theory on Abelian-Quotient V-Surfaces and Q-Resolutions
cites work: The Decomposition Theorem for V-Manifolds
cites work: Local invariants on quotient singularities and a genus formula for weighted plane curves
cites work: Q5623820
cites work: Théorie de Hodge. II. (Hodge theory. II)
cites work: Théorie de Hodge. III
cites work: 2-Jordan blocks for the eigenvalue \(\lambda = 1\) of Yomdin-Lê surface singularities
cites work: Embedded \(\mathbf Q\)-resolutions for Yomdin-Lê surface singularities
cites work: Partial resolutions and the zeta-function of a singularity
cites work: Toroidal embeddings. I
cites work: Monodromy zeta function formula for embedded \(\mathbf{Q}\)-resolutions
cites work: ON A GENERALIZATION OF THE NOTION OF MANIFOLD
cites work: Variation of Hodge structure: The singularities of the period mapping
cites work: Q4011180
cites work: Q5519950
cites work: Q5203151
cites work: Motivic Milnor Fibre for Nondegenerate Function Germs on Toric Singularities
cites work: Q3933097
cites work: Complex surfaces with a one-dimensional set of singularities
DOI: 10.1007/S10231-015-0546-3
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description: scientific article; zbMATH DE number 6637358