SET-THEORETIC COMPLETE INTERSECTIONS ON BINOMIALS, THE SIMPLICIAL TORIC CASE

Autores/as

  • Margherita Barile CSI-UNMSM
  • Marcel Morales Université de Grenoble I, lnstitut Fourier, URA 188, B.P. 74, 38402 Saint-Martin D'Heres Cedex, and IUFM de Lyon, 5 rue Anselme, 69317 Lyon Cedex (France)
  • Apostolos Thoma Department of Mathematics, University of Ioannína, Ioannina 45110 (Greece)

DOI:

https://doi.org/10.15381/pes.v3i2.9245

Resumen

Let V be a simplicial toric variety of codimension r over a field of any characteristic. We completely characterize the implicial toric varieties that are set-theoretic complete intersections on binomials. In particular we prove that:
1. In characteristic zero, V is a set-theoretic complete intersection on binomials if and only jf V is a. complete intersection.  Moreover, if F1,…,Fr; are binomials such that I(V)= rad( F1, . .. ,Fr), th en I(V) = (F1, ... ,Fr).
We also get a geometric proof of some of the results in [9] characterizing complete intersections by gluing; semigroups.
2. In positive characteristic p, V is a set-theoretic complete intersection on binomials if and only if V is complete 1y p-glued. These results improve and complete all known results on these topics.

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Publicado

2000-12-29

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SET-THEORETIC COMPLETE INTERSECTIONS ON BINOMIALS, THE SIMPLICIAL TORIC CASE. (2000). Pesquimat, 3(2). https://doi.org/10.15381/pes.v3i2.9245