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Numerically Testing Generically Reduced Projective Schemes for the Arithmetic Gorenstein Property

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Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

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Abstract

Let \(X\subset {\mathbb P}^n\) be a generically reduced projective scheme. A fundamental goal in computational algebraic geometry is to compute information about X even when defining equations for X are not known. We use numerical algebraic geometry to develop a test for deciding if X is arithmetically Gorenstein and apply it to three secant varieties.

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Acknowledgments

The authors would like to thank Luke Oeding for helpful discussions. Both authors were supported in part by DARPA Young Faculty Award (YFA) and NSF grant DMS-1262428. JDH was also supported by Sloan Research Fellowship and NSF ACI-1460032.

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Authors and Affiliations

  1. Department of Mathematics, Worcester State University, Worcester, MA, 01602, USA

    Noah S. Daleo

  2. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Jonathan D. Hauenstein

Authors
  1. Noah S. Daleo
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  2. Jonathan D. Hauenstein
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Correspondence to Noah S. Daleo .

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Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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Daleo, N.S., Hauenstein, J.D. (2016). Numerically Testing Generically Reduced Projective Schemes for the Arithmetic Gorenstein Property. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_11

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

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