Numerically Testing Generically Reduced Projective Schemes for the Arithmetic Gorenstein Property

  • Noah S. DaleoEmail author
  • Jonathan D. Hauenstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)


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.



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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsWorcester State UniversityWorcesterUSA
  2. 2.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA

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