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Vector Fields and the Cohomology Ring of Toric Varieties

  • Autores: Kiumars Kaveh
  • Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 3, 2005, págs. 414-427
  • Idioma: inglés
  • DOI: 10.4153/cmb-2005-039-1
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • Let X be a smooth complex projective variety with a holomorphic vector field with isolated zero set Z. From the results of Carrell and Lieberman there exists a filtration F0 subset F1 subset ... of A(Z), the ring of mathbb C-valued functions on Z, such that Gr A(Z) \cong H*(X, mathbb C) as graded algebras. In this note, for a smooth projective toric variety and a vector field generated by the action of a 1-parameter subgroup of the torus, we work out this filtration. Our main result is an explicit connection between this filtration and the polytope algebra of X.


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