TY - RPRT T1 - Q-factorial Laurent rings Y1 - 2011 A1 - Ugo Bruzzo A1 - Antonella Grassi AB - Dolgachev proved that, for any field k, the ring naturally associated to a\\r\\ngeneric Laurent polynomial in d variables, $d \\\\geq 4$, is factorial. We prove a\\r\\nsufficient condition for the ring associated to a very general complex Laurent\\r\\npolynomial in d=3 variables to be Q-factorial. PB - SISSA UR - http://hdl.handle.net/1963/4183 N1 - 5 pages U1 - 3907 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - RPRT T1 - Picard group of hypersurfaces in toric varieties Y1 - 2010 A1 - Ugo Bruzzo A1 - Antonella Grassi AB - We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds. UR - http://hdl.handle.net/1963/4103 U1 - 301 U2 - Mathematics U3 - Mathematical Physics ER -