Abstract:
In this paper the author presents an approach to the problem of classifying quasihomogeneous singularities, based on the use of simple properties of deformation theories of such singularities. By means of Grothendieck local duality the Poincaré series of the space of the first cotangent functor T1 of a one-dimensional singularity is computed. Lists of normal forms and monomial bases of the spaces of T1 are given for one-dimensional quasihomogeneous complete intersections with inner modality 0 and 1, and also with Milnor number less than seventeen. An adjacency diagram is constructed for all singularities that have been found.
Bibliography: 33 titles.
\Bibitem{Ale82}
\by A.~G.~Aleksandrov
\paper Normal forms of one-dimensional quasihomogeneous complete intersections
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 1
\pages 1--30
\mathnet{http://mi.mathnet.ru/eng/sm1859}
\crossref{https://doi.org/10.1070/SM1983v045n01ABEH000989}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=642486}
\zmath{https://zbmath.org/?q=an:0548.14017|0508.14001}
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https://www.mathnet.ru/eng/sm1859
https://doi.org/10.1070/SM1983v045n01ABEH000989
https://www.mathnet.ru/eng/sm/v159/i1/p3
This publication is cited in the following 10 articles:
A. G. Aleksandrov, “Differential Forms on Zero-Dimensional Singularities”, Funct. Anal. Appl., 52:4 (2018), 241–257
Katsusuke Nabeshima, Katsuyoshi Ohara, Shinichi Tajima, “Comprehensive Gröbner systems in PBW algebras, Bernstein–Sato ideals and holonomic D-modules”, Journal of Symbolic Computation, 89 (2018), 146
Katsusuke Nabeshima, Shinichi Tajima, “Algebraic local cohomology with parameters and parametric standard bases for zero-dimensional ideals”, Journal of Symbolic Computation, 82 (2017), 91
Aleksandrov A., “Modular Space for Complete Intersection Curve-Singularities”, Finite Or Infinite Dimensional Complex Analysis, Lecture Notes in Pure and Applied Mathematics, 214, eds. Kajiwara J., Li Z., Shon KH., Marcel Dekker, 2000, 1–19
S. Hosono, A. Klemm, S. Thiesen, S-T Yau, “Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces”, Comm Math Phys, 167:2 (1995), 301
A. G. Aleksandrov, “Vector fields on a complete intersection”, Funct. Anal. Appl., 25:4 (1991), 283–284
A. G. Aleksandrov, “Nonisolated Saito singularities”, Math. USSR-Sb., 65:2 (1990), 561–574
A. G. Aleksandrov, “A de Rahm complex of nonisolated singularities”, Funct. Anal. Appl., 22:2 (1988), 131–133
A. G. Aleksandrov, “Cohomology of a quasihomogeneous complete intersection”, Math. USSR-Izv., 26:3 (1986), 437–477
A. G. Aleksandrov, “The de Rham complex of a quasihomogeneous complete intersection”, Funct. Anal. Appl., 17:1 (1983), 48–49
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