A note on monomial ideals

We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms of the number of its minimal monomial generators and the maximal height of its minimal primes

A note on the edge ideals of Ferrers graphs

We determine the arithmetical rank of every edge ideal of a Ferrers graph

A note on Veronese varieties

We show that for every prime $p$, there is a class of Veronese varieties which are set-theoretic complete intersections if and only if the ground field has characteristic $p$

On the arithmetical rank of a special class of minimal varieties

We study the arithmetical ranks and the cohomological dimensions of an infinite class of Cohen-Macaulay varieties of minimal degree. Among these we find, on the one hand, infinitely many set-theoretic complete intersections, on the other hand examples where the arithmetical rank is arbitrarily greater than the codimension.Comment: The first part of Section 4 was rewritte

On simplicial toric varieties of codimension 2

We describe classes of toric varieties of codimension 2 which are either minimally defined by 3 binomial equations over any algebraically closed field, or are set-theoretic complete intersections in exactly one positive characteristic.Comment: Revised version. To appear in: Rendiconti dell'Istituto di Matematica dell'Universita' di Trieste. Dedicated to the memory of Fabio Ross

On binomial set-theoretic complete intersections in characteristic p

Using aritmethic conditions on affine semigroups we prove that for a simplicial toric variety of codimension 2 the property of being a set-theoretic complete intersection on binomials in characteristic $p$ holds either for all primes $p$, or for no prime $p$, or for exactly one prime $p$