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Trudy Mat. Inst. Steklova, 2009, Volume 267, Pages 119–131 (Mi tm2601)  

This article is cited in 12 scientific papers (total in 12 papers)

On Indices of 1-Forms on Determinantal Singularities

S. M. Gusein-Zadea, W. Ebelingb

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Institut für Algebraische Geometrie, Leibniz Universität Hannover, Hannover, Germany

Abstract: We consider 1-forms on so-called essentially isolated determinantal singularities (a natural generalization of isolated singularities), show how to define analogs of the Poincaré–Hopf index for them, and describe relations between these indices and the radial index. For isolated determinantal singularities, we discuss properties of the homological index of a holomorphic 1-form and its relation to the Poincaré–Hopf index.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 267, 113–124

Bibliographic databases:

UDC: 512.761.5
Received in July 2008

Citation: S. M. Gusein-Zade, W. Ebeling, “On Indices of 1-Forms on Determinantal Singularities”, Singularities and applications, Collected papers, Trudy Mat. Inst. Steklova, 267, MAIK Nauka/Interperiodica, Moscow, 2009, 119–131; Proc. Steklov Inst. Math., 267 (2009), 113–124

Citation in format AMSBIB
\by S.~M.~Gusein-Zade, W.~Ebeling
\paper On Indices of 1-Forms on Determinantal Singularities
\inbook Singularities and applications
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2009
\vol 267
\pages 119--131
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2009
\vol 267
\pages 113--124

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    This publication is cited in the following articles:
    1. Nuno-Ballesteros J.J., Orefice-Okamoto B., Tomazella J.N., “The Vanishing Euler Characteristic of an Isolated Determinantal Singularity”, Isr. J. Math., 197:1 (2013), 475–495  crossref  mathscinet  zmath  isi  scopus
    2. Soares Ruas M.A., Pereira Miriam Da Silva, “Codimension Two Determinantal Varieties With Isolated Singularities”, Math. Scand., 115:2 (2014), 161–172  crossref  mathscinet  zmath  isi  scopus
    3. A. G. Aleksandrov, “Differential Forms on Quasihomogeneous Noncomplete Intersections”, Funct. Anal. Appl., 50:1 (2016), 1–16  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Ament D.A.H., Nuno-Ballesteros J.J., Orefice-Okamoto B., Tomazella J.N., “The Euler obstruction of a function on a determinantal variety and on a curve”, Bull. Braz. Math. Soc., 47:3 (2016), 955–970  crossref  mathscinet  zmath  isi  elib  scopus
    5. Brasselet J.-P., Chachapoyas N., Ruas M.A.S., “Generic Sections of Essentially Isolated Determinantal Singularities”, Int. J. Math., 28:11 (2017), 1750083  crossref  mathscinet  zmath  isi  scopus
    6. Chachapoyas Siesquen N.C., “Euler Obstruction of Essentially Isolated Determinantal Singularities”, Topology Appl., 234 (2018), 166–177  crossref  mathscinet  zmath  isi  scopus
    7. Fruehbis-Krueger A., “On Discriminants, Tjurina Modifications and the Geometry of Determinantal Singularities”, Topology Appl., 234 (2018), 375–396  crossref  mathscinet  zmath  isi  scopus
    8. Kerner D., Pedersen H.M., Ruas M.A.S., “Lipschitz Normal Embeddings in the Space of Matrices”, Math. Z., 290:1-2 (2018), 485–507  crossref  mathscinet  isi  scopus
    9. da Silva T.F., Grulha Jr. Nivaldo G., Pereira M.S., “The Bi-Lipschitz Equisingularity of Essentially Isolated Determinantal Singularities”, Bull. Braz. Math. Soc., 49:3 (2018), 637–645  crossref  mathscinet  zmath  isi  scopus
    10. Ahmed I., Soares Ruas M.A., “Determinacy of Determinantal Varieties”, Manuscr. Math., 159:1-2 (2019), 269–278  crossref  mathscinet  zmath  isi  scopus
    11. Gaffney T., Grulha Jr. Nivaldo G., Ruas M.A.S., “The Local Euler Obstruction and Topology of the Stabilization of Associated Determinantal Varieties”, Math. Z., 291:3-4 (2019), 905–930  crossref  mathscinet  zmath  isi  scopus
    12. Zach M., “Bouquet Decomposition For Determinantal Milnor Fibers”, J. Singul., 22 (2020), 190–204  crossref  mathscinet  isi
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