Professor Paolo Cascini

P Cascini, G La Nave, 2005, Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties.

In this note we propose to show that the Kähler-Ricci flow fits naturally within the context of the Minimal Model Program for projective varieties. In particular we show that the flow detects, in finite time, the contraction theorem of any extremal ray and we analyze the singularities of the metric in the case of divisorial contractions for varieties of general type. In case one has a smooth minimal model of general type (i.e., the canonical bundle is nef and big), we show infinite time existence and analyze the singularities.

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Cascini P, 2002, On the moduli space of the Schwarzenberger bundles, PACIFIC JOURNAL OF MATHEMATICS, Vol: 205, Pages: 311-323, ISSN: 0030-8730

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Cascini P, 2001, Weighted Tango bundles on IP<i><SUP>n</SUP></i> and their moduli spaces, FORUM MATHEMATICUM, Vol: 13, Pages: 251-260, ISSN: 0933-7741

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Cascini P, 1999, On a compactification of the moduli space of the rational normal curves

For any odd $n$, we describe a smooth minimal (i.e. obtained by adding anirreducible hypersurface) compactification $\tilde S_n$ of the quasi-projectivehomogeneous variety $S_{n}=PGL(n+1)/SL(2)$ that parameterizes the rationalnormal curves in $P^n$. We show that $\tilde S_{n}$ is isomorphic to acomponent of the Maruyama scheme of the semi-stable sheaves on $P^n$ of rank$n$ and Chern polynomial $(1+t)^{n+2}$ and we compute its Betti numbers. In particular $\tilde S_{3}$ is isomorphic to the variety of nets of quadricsdefining twisted cubics, studied by G. Ellinsgrud, R. Piene and S. Str{\o}mme(Space curves, Proc. Conf., LNM 1266).

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