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2 results

  • THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA

  • Part of
  • I. OJEDA, A. VIGNERON-TENORIO
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 96 / Issue 3 / December 2017
    Published online by Cambridge University Press:
    29 August 2017, pp. 400-411
    Print publication:
    December 2017
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  • This work generalises the short resolution given by Pisón Casares [‘The short resolution of a lattice ideal’, Proc. Amer. Math. Soc.131(4) (2003), 1081–1091] to any affine semigroup. We give a characterisation of Apéry sets which provides a simple way to compute Apéry sets of affine semigroups and Frobenius numbers of numerical semigroups. We also exhibit a new characterisation of the Cohen–Macaulay property for simplicial affine semigroups.

  • Derivation Algebras of Toric Varieties

  • ANTONIO CAMPILLO, JANUSZ GRABOWSKI, GERD MÜLLER
  • Journal:
    Compositio Mathematica / Volume 116 / Issue 2 / April 1999
    Published online by Cambridge University Press:
    04 December 2007, pp. 119-132
    Print publication:
    April 1999
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  • We study the Lie algebra of derivations of the coordinate ring of affine toric varieties defined by simplicial affine semigroups and prove the following results:

    Such toric varieties are uniquely determined by their Lie algebra if they are supposed to be Cohen–Macaulay of dimension [ges ] 2 or Gorenstein of dimension =1.

    In the Cohen–Macaulay case, every automorphism of the Lie algebra is induced from a unique automorphism of the variety.

    Every derivation of the Lie algebra is inner.