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Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

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Developments and Retrospectives in Lie Theory

Part of the book series: Developments in Mathematics ((DEVM,volume 38))

Abstract

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.

Work supported by the Australian Research Council.

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Notes

  1. 1.

    The proof of this proposition given in [6] was suggested to us by A. Gorinov.

  2. 2.

    This formula for the discriminant of a ternary cubic differs from the general formula given in [12] by a scalar factor.

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Author information

Authors and Affiliations

  1. Mathematical Sciences Institute, The Australian National University, Canberra, ACT, 0200, Australia

    Michael Eastwood & Alexander Isaev

Authors
  1. Michael Eastwood
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  2. Alexander Isaev
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Corresponding author

Correspondence to Michael Eastwood .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, Santa Cruz, Santa Cruz, California, USA

    Geoffrey Mason

  2. Jacobs University, Bremen, Germany

    Ivan Penkov

  3. Department of Mathematics, University of California, Berkeley, Berkeley, California, USA

    Joseph A. Wolf

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Eastwood, M., Isaev, A. (2014). Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities. In: Mason, G., Penkov, I., Wolf, J. (eds) Developments and Retrospectives in Lie Theory. Developments in Mathematics, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-09804-3_7

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