Castelnuovo¿Mumford regularity of projective monomial varieties of codimension two

• Autores: Marcel Morales , Philippe Giménez , María Isabel Bermejo Díaz
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 10, 2006, págs. 1105-1124
• Idioma: inglés
• DOI: 10.1016/j.jsc.2006.06.006
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• Resumen

  • Let K be an algebraically closed field, and let be a projective monomial variety of codimension two with n=2, i.e., a projective toric variety of codimension two whose homogeneous coordinate ring is a simplicial semigroup ring. We give an explicit formula for the Castelnuovo¿Mumford regularity of , , in terms of the reduced Gröbner basis of with respect to the reverse lexicographic order. As a consequence, we show that , where is the degree of , and characterize when equality holds.