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On some numerical properties of Fano varieties

Cinzia Casagrande (2004)

Bollettino dell'Unione Matematica Italiana

This is the text of a talk given at the XVII Convegno dell’Unione Matematica Italiana held at Milano, September 8-13, 2003. I would like to thank Angelo Lopez and Ciro Ciliberto for the kind invitation to the conference. I survey some numerical conjectures and theorems concerning relations between the index, the pseudo-index and the Picard number of a Fano variety. The results I refer to are contained in the paper [3], wrote in collaboration with Bonavero, Debarre and Druel.

On some properties of partial intersection schemes.

Alfio Ragusa, Giuseppe Zappalà (2003)

Collectanea Mathematica

Partial intersection subschemes of Pr of codimension c were used to furnish various graded Betti numbers which agree with a fixed Hilbert function. Here we study some further properties of such schemes; in particular, we show that they are not in general licci and we give a large class of them which are licci. Moreover, we show that all partial intersections are glicci. We also show that for partial intersections the first and the last Betti numbers, say m and p respectively, give bounds each other;...

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