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On the Gauss algebra of toric algebras

  • Jürgen HerzogEmail author
  • Raheleh Jafari
  • Abbas Nasrollah Nejad
Article
  • 93 Downloads

Abstract

Let A be a K-subalgebra of the polynomial ring \(S=K[x_1,\ldots ,x_d]\) of dimension d, generated by finitely many monomials of degree r. Then, the Gauss algebra \({\mathbb {G}}(A)\) of A is generated by monomials of degree \((r-1)d\) in S. We describe the generators and the structure of \({\mathbb {G}}(A)\), when A is a Borel fixed algebra, a squarefree Veronese algebra, generated in degree 2, or the edge ring of a bipartite graph with at least one loop. For a bipartite graph G with one loop, the embedding dimension of \({\mathbb {G}}(A)\) is bounded by the complexity of the graph G.

Keywords

Gauss map Gauss algebra Birational morphism Borel fixed algebra Squarefree Veronese algebra Edge ring 

Mathematics Subject Classification

13C15 14M25 05E40 05C50 14E05 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Jürgen Herzog
    • 1
    Email author
  • Raheleh Jafari
    • 2
  • Abbas Nasrollah Nejad
    • 3
  1. 1.Fachbereich MathematikUniversität Duisburg-EssenEssenGermany
  2. 2.Mosaheb Institute of MathematicsKharazmi University, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM)TehranIran
  3. 3.Department of MathematicsInstitute for Advanced Studies in Basic Sciences (IASBS)ZanjanIran

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