On a special class of simplicial toric varieties

We show that for all $n\geq 3$ and all primes $p$ there are infinitely many simplicial toric varieties of codimension $n$ in the $2n$-dimensional affine space whose minimum number of defining equations is equal to $n$ in characteristic $p$, and lies between $2n-2$ and $2n$ in all other characteristics. In particular, these are new examples of varieties which are set-theoretic complete intersections only in one positive characteristic.\newline Moreover, we show that the minimum number of binomial equations which define these varieties in all characteristics is 4 for $n=3$ and $2n-2+{n-2\choose 2}$ whenever $n\geq 4$

On toric varieties which are almost set-theoretic complete intersections

We describe a class of affine toric varieties $V$ that are set-theoretically minimally defined by codim $V+1$ binomial equations over fields of any characteristic

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 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

A note on the edge ideals of Ferrers graphs

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