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Numerical characterization of nef arithmetic divisors on arithmetic surfaces

Atsushi Moriwaki (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper, we give a numerical characterization of nef arithmetic -Cartier divisors of C 0 -type on an arithmetic surface. Namely an arithmetic -Cartier divisor D ¯ of C 0 -type is nef if and only if D ¯ is pseudo-effective and deg ^ ( D ¯ 2 ) = vol ^ ( D ¯ ) .

Numerical semigroups with a monotonic Apéry set

José Carlos Rosales, Pedro A. García-Sánchez, Juan Ignacio García-García, M. B. Branco (2005)

Czechoslovak Mathematical Journal

We study numerical semigroups S with the property that if m is the multiplicity of S and w ( i ) is the least element of S congruent with i modulo m , then 0 < w ( 1 ) < < w ( m - 1 ) . The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.

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