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Mosc. Math. J., 2003, Volume 3, Number 2, Pages 361–395 (Mi mmj91)  

This article is cited in 5 scientific papers (total in 5 papers)

On the legacy of free divisors. II. Free* divisors and complete intersections

J. Damon

Department of Mathematics, University of North Carolina at Chapel Hill

Abstract: We provide a criterion that for an equivalence group $\mathcal G$ on holomorphic germs, the discriminant of a $\mathcal G$-versal unfolding is a free divisor. The criterion is in terms of the discriminant being Cohen–Macaulay and generically having Morse-type singularities. When either of these conditions fails, we provide a criterion that the discriminant have a weaker free* divisor structure. For nonlinear sections of a free* divisor $V$, we obtain a formula for the number of singular vanishing cycles by modifying an earlier formula obtained with David Mond and taking into account virtual singularities.

Key words and phrases: Discriminants, versal unfoldings, free divisors, free* divisors, liftable vector fields, Morse-type singularities, Cohen–Macaulay condition.

DOI: https://doi.org/10.17323/1609-4514-2003-3-2-361-395

Full text: http://www.ams.org/.../abst3-2-2003.html
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Bibliographic databases:

MSC: Primary 14B07, 14M12, 32S30; Secondary 16G50, 14J17
Received: May 15, 2002
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Citation: J. Damon, “On the legacy of free divisors. II. Free* divisors and complete intersections”, Mosc. Math. J., 3:2 (2003), 361–395

Citation in format AMSBIB
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\by J.~Damon
\paper On the legacy of free divisors. II.~Free* divisors and complete intersections
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 2
\pages 361--395
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\crossref{https://doi.org/10.17323/1609-4514-2003-3-2-361-395}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Damon J., “On the legacy of free divisors III: Functions and divisors on complete intersections”, Quarterly Journal of Mathematics, 57:1 (2006), 49–79  crossref  mathscinet  zmath  isi
    2. Buchweitz R.-O., Ebeling W., von Bothmer H.-Ch.G., “Low-Dimensional Singularities with Free Divisors as Discriminants”, Journal of Algebraic Geometry, 18:2 (2009), 371–406  crossref  mathscinet  zmath  isi
    3. Damon J., Pike B., “Solvable group representations and free divisors whose complements are K(pi, 1)'s”, Topology Appl, 159:2 (2012), 437–449  crossref  mathscinet  zmath  isi
    4. Damon J. Pike B., “Solvable Groups, Free Divisors and Nonisolated Matrix Singularities i: Towers of Free Divisors”, Ann. Inst. Fourier, 65:3 (2015), 1251–1300  crossref  mathscinet  zmath  isi
    5. Nabeshima K., Tajima Sh., “Computation Methods of Logarithmic Vector Fields Associated to Semi-Weighted Homogeneous Isolated Hypersurface Singularities”, Tsukuba J. Math., 42:2 (2018), 191–231  crossref  mathscinet  zmath  isi
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