Searcharxiv⌕ Search

arXiv subjects

Claudio Fontanari

Publications and source records attributed to Claudio Fontanari.

64 records · Page 4Linked to original sources
arXiv2004

Moduli of Curves and Spin Structures via Algebraic Geometry

Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type (p,0) and on computations of the Kodaira dimension. Our methods are purely algebraic geometric and rely on an induction argument on the number of marked points and the genus of the curves (cf. mathAG/9803001).

math.AG↗
arXiv2004

On Waring's problem for partially symmetric tensors

Here we address a Waring type problem for partially symmetric tensors, extending previous work by Massimiliano Mella in the totally symmetric case of forms. In particular, we provide an explicit answer in lower dimensional cases.

math.AG↗
arXiv2004

On a Lemma of Bompiani

We reprove in modern terms and extend to arbitrary dimension a classical result of Enrico Bompiani on algebraic surfaces $X \subset \PP^r$ having very degenerate osculating spaces.

math.AG↗
arXiv2004

Birational geometry of defective varieties

Here we investigate the birational geometry of projective varieties of arbitrary dimension having defective higher secant varieties. We apply the classical tool of tangential projections and we determine natural conditions for uniruledness, rational connectivity, and rationality.

math.AG↗
arXiv2004

Moduli of Prym curves

Here we focus on the compactification of the moduli space of curves of genus g together with an unramified double cover, constructed by Arnaud Beauville in order to compactify the Prym mapping. We present an alternative description of it, inspired by the moduli space of spin curves of Maurizio Cornalba, and we discuss in detail its main features, both from a geometrical and a combinatorial point of view.

math.AG↗
arXiv2004

On the geometry of the compactification of the universal Picard variety

Here we focus on the geometry of $\pdgbar$, 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 $\pdgbar$ and we give generators and relations of the rational divisor class group of $\pdgbar$, extending previous work by A. Kouvidakis.

math.AG↗
arXiv2004

On the surjectivity of the canonical Gaussian map for multiple coverings

Here we investigate the canonical Gaussian map for higher multiple coverings of curves, the case of double coverings being completely understood thanks to previous work by Duflot. In particular, we prove that every smooth curve can be covered with degree not too high by a smooth curve having arbitrarily large genus and surjective canonical Gaussian map. As a consequence, we recover an asymptotic version of a recent result by Ciliberto and Lopez and we address the Arbarello subvariety in the moduli space of curves.

math.AG↗
arXiv2001

Grassmann defectivity à la Terracini

This work is a modern revisitation of a classical paper by Alessandro Terracini, going back to 1915, which suggests an elementary but powerful method for studing Grassmann defective varieties. In particular, the case of Veronese surfaces is completely understood, giving an positive answer to the so-called Waring problem for pairs of homogeneous polynomials in three variables.

math.AG↗