Abstract
In this paper, we study the generators of the module of derivations of certain hypersurfaces and obtain bounds on their minimum number of generators.
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References
Brennar J, Herzog J and Ulrich B, Maximally generated Cohen–Macaulay modules, Math. Scand. 61 (1987) 181–203
Herzog J and Kühl M, Maximal Cohen–Macaulay modules over Gorenstein rings and Bourbaki sequences, Commutative Algebra and Combinatorics, Kyoto, 1985, Adv. Stud. Pure Math., vol. 11 (1987) (Amsterdam: North-Holland) pp. 65–92
Krämer H, Eine Bemerkung zu einer Vermutung von Lipman, Arch. Math. 20 (1969) 30–35
Kuan W E, A note on a lemma of Zariski and higher derivations, Proc. Am. Math. Soc. 42 (1974) 333–340
Liu Y, Milnor and Tjurina numbers for a hypersurface germ with isolated singularity, C. R. Acad. Sci. Paris, Ser. I 356 (2018) 963–966
Milnor J, Singular points of complex hypersurfaces (1968) (Princeton: Princeton University Press)
Miranda-Neto Cleto B, Graded derivation modules and algebraic free divisors, J. Pure Appl. Algebra 219(12) (2015) 5442–5466
Patil D P and Singh B, Generators for the derivation modules and the relation ideals of certain curves, Manuscr. Math. 68 (1990) 327–335
Saito K, Quasihomogene isolierte Singularitäten von Hyperflächen, Inventiones Math. 14 (1971) 123–142
Scheja G and Storch U, Differentielle Eigenschaften der Lokalisierungen analytischer Algebren, Math. Ann. 197 (1972) 137–170
Schoutens H, Number of generators of a Cohen–Macaulay ideal, J. Algebra 259(1) (2003) 235–242
Serre J P, Sur les modules projectifs (Algébre et théorie des nombres), Séminaire Dubreil, M-L Dubreil-Jacotin et C Pisot, 1957/1958, Fasc. 2, Exposé 23, No. 2, Secrétariat mathématique, 1960–1961
Vasconcelos W V, Reflexive modules over Gorenstein rings, Proc. Am. Math. Soc. 19 (1968) 1349–1355
Zariski O and Samuel P, Commutative Algebra, D. Van Nostrand Co Inc., vol. 1 (1958)
Acknowledgements
The first author (RVG) is thankful to the Indian National Science Academy for a fellowship during this work. The second author (AP) is thankful to the National Board for Higher Mathematics, Department of Atomic Energy, India, for a scholarship during this work. The authors would like to thank the referee for valuable comments and remarks in improving the presentation of this paper.
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Communicated by Mrinal Kanti Das.
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Gurjar, R.V., Patra, A. Number of generators of derivation modules of some hypersurfaces. Proc Math Sci 132, 39 (2022). https://doi.org/10.1007/s12044-022-00689-0
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DOI: https://doi.org/10.1007/s12044-022-00689-0