Università degli Studi di Torino
DOTTORATO DI RICERCA IN MATEMATICA

My research is mainly devoted to Algebraic Geometry, in particular I study some topics concerning zero-dimensional schemes.

Gorenstein Ideals On the years 2000 and 2001 my attention was in particular addressed to the Liaison Theory and the construction of Gorenstein Ideals. In a joint work with Giorgio Dalzotto (Univ. of Pisa) we were able to construct some particular zero-dimensional Gorenstein schemes in P^3: these schemes arises from the union of the residual of a complete intersection with a well-choose new complete intersection ([1]). Prof A.V. Geramita proposed us a second publication of the same article on Queen's Papers, but enriched of examples related to another constructions ([2]). After a while, in a joint work with Roberto Notari and Maria Luisa Spreafico, we were able to generalize these results to the case of codimension 3 in every space (i.e, not necessarily points in P^3) and to the case of every codimension ([3]). The last case is quite important because the knowledge of this kind of Gorenstein ideals is still very limited: we don't know, for example, the behaviour of their Hilbert function.

Polynomial Interpolation in Algebraic Geometry On 2001 I started to work to my Ph.D. thesis under the supervision of Rick Miranda and Luca Chiantini. My research is so devoted to special linear systems and the Segre and Harbourne-Hirschowitz conjectures. In particular we defined a kind of variety, the \alpha-SEV, in such a way to generalize the concept of (-1)-curves for special systems in P^r, r>2 and to state the following conjecture: "a system is special if and only if its speciality arises from the existence of a \alpha-SEV" At the same time, Ciliberto and Miranda proposed a similar conjecture related to the existence of another class of variety, the so-called h^1-SEV. I recently showed that, in the planar case, the previous four conjectures are equivalent.

Fat Points on Ruled Varieties This topic is strictly related to the previous one. In a joint work with Ballico and Fontanari ([4]) we analyzed fat points of multiplicity 2 and 3 on ruled surfaces. Moreover we state two different questions about the independency of conditions imposed by fat points on a general ruled varieties. Here, we give the idea for the study of systems, whose restrictions to the fiber F satisfy some particular conditions on the degree.
 
 

1. Bocci, Dalzotto: Gorenstein Points in P^3, Rendiconti del Seminario Matematico dell' Università e del Politecnico di Torino, 59, num 2, pages 155-164 (2001)
2. Bocci, Dalzotto: Reduced Arithmetically Gorenstein Schemes of Codimension 3, accepted for the publication on "Queen's Papers in Pure and Applied Mathematics"
3. Bocci, Dalzotto, Notari, Spreafico: An Iterative Construction of Gorenstein Ideals, submitted to "Transactions of AMS"
4. Ballico, Bocci, Fontanari: Zero-Dimensional Schemes of Ruled Varieties, submitted to ECJM
5. Bocci: Special Systems, (-1)-curves and Special Effect Varieties, work in Progress

	Università degli Studi di Torino  Dipartimento di Matematica pagina realizzata da Cristiano Bocci		Palazzo Campana Via Carlo Alberto, 10 10123 Torino Tel.:+39 011 670.2827  Fax: +39 011 670.2878
	Ultimo aggiornamento: 30 Giugno 2003