A projective variety is -defective if the Grassmannian of lines contained in the span of independent points on has dimension less than the expected one. In the present paper, which is inspired by classical work of Alessandro Terracini, we prove a criterion of -defectivity for algebraic surfaces and we discuss its applications to Veronese embeddings and to rational normal scrolls.
We investigate deformation-theoretical properties of curves carrying a half-canonical linear series of fixed dimension. In particular, we improve the previously known bound on the dimension of the corresponding loci in the moduli space and we obtain a natural description of the tangent space to higher theta loci.
Here we focus on the geometry of , the compactification of the universal Picard variety constructed by L. Caporaso. In particular, we show that the moduli space of spin curves constructed by M. Cornalba naturally injects into and we give generators and relations of the rational Picard group of , extending previous work by A. Kouvidakis.
Il matematico Enrico Arbarello, ex studente di Emma alle scuole medie inferiori, condivide ricordi e osservazioni a proposito dei metodi didattici della sua insegnante.
We explore the geometry of the osculating spaces to projective verieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the existence of inflectionary points.
Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying the Horace method and the Terracini method
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