VALERIO BUTTINELLI

Dottore di ricerca

ciclo: XXXVIII


supervisore: Prof. M. Manetti
relatore: Prof. A. F. Lopez

Titolo della tesi: On the positivity of Ulrich bundles

We study the positivity properties of Ulrich bundles defined with respect to an ample and globally generated polarization. First we prove a generalization of a theorem by Lopez on the first Chern class. Then, under some additional assumptions on the polarization, we give a description of its augmented base locus, which consequently leads to a characterization of the V-bigness and of the ampleness of an Ulrich bundle in this setting. Finally we study the normal generation of an Ulrich bundle focusing on curves, on surfaces with q=p_g=0 and on hypersurfaces of dimension 2 and 3.

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