Lucio Guerra

On rational maps from a general surface in to surfaces of general type

We study the dominant rational maps from a general surface in P^{3} to surfaces of general type. We prove restrictions on the target surfaces, and special properties of the rational maps. We show that for a small degree the general surface has no such map. Moreover a slight improvement of a result of Catanese, on the number of moduli of a surface of general type, is also obtained.

On the Linear Codes Arising from Schubert Varieties

We prove a lower bound for the minimum distance of the linear code associated to a Schubert variety. Moreover for a Schubert variety of lines we compute the full distribution of weights.

On the finiteness theorem for rational maps on a variety of general type

The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in virtue of some recent advances in the theory of pluricanonical maps. We study the question of finding some effective estimate for the finite number of maps, and to this aim we provide some update and refinement of the classical treatment of the subject.

Orbits of Lagrangian Subalgebras of the Double sl(2, R)

We describe the variety of Lagrangian subalgebras of the Drinfeld double for an arbitrary bialgebra structure on sl(2, R). We determine the irreducible components and the orbit structure under the natural action of the group SL(2, R)