Riccardo Re

Multiplication of sections and Clifford bounds for stable vector bundles on curves

A sharp lower bound for the rank of the natural multiplication map H 0(F) ⊗ H 0(G) → H 0(F⊗ G) is givenFand Gbeing vector bundles generically generated by their global sections on an integral projective variety.Some Clifford-type inequalities in the context of the Brill-Noether theory of vector bundles on a curve are proved and their sharpness is studied.

Relational Representation of Groupoid Quantales

In Palmigiano and Re (J Pure Appl Algebra 215(8):1945–1957, 2011), spatial SGF-quantales are axiomatically introduced and proved to be representable as sub unital involutive quantales of quantales arising from set groupoids. In the present paper, spatial SGF-quantales of this class are shown to be optimally representable as unital involutive quantales of relations. The results of the present paper have several aspects in common with Jónsson and Tarski’s representation theory for relation algebras (Jónsson and Tarski, Am J Math 74(2):127–162, 1952).

An algorithm for the normal bundle of rational monomial curves

We give a method to calculate the cohomology of the twisted normal bundle over a smoth rational curve. From this method we derive a vanishing result and an algorithm for calculating the splitting type of the bundle for any rational monomial curve.

Supersingular quotients of Fermat curves

We give formulas for the genera of all the possible quotient of a Fermat curve by a group of automorphisms in characteristic zero and for many classes of quotient curves also in positive characteristic. We use those results for giving evidence to the conjecture that, in any fixed positive characteristic, there should exist supersingular curves for any genus.

Complete intersections of quadrics and the Weak Lefschetz Property

We consider graded artinian complete intersection algebras

On the maximum rank of a real binary form

A=\mathbb {C}[x_0,\ldots ,x_m]/I

Some remarks on linear spaces of nilpotent matrices

A=C[x0,…,xm]/I with I generated by homogeneous forms of degree