University of Florence

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20022009

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math.AG2009★ 5 cited

Non-Defectivity of Grassmannians of planes

Hirotachi Abo, Giorgio Ottaviani, Chris Peterson

Let $G r (k, n)$ be the Plücker embedding of the Grassmann variety of projective $k$ -planes in $¶ n$ . For a projective variety $X$ , let $σ_{s} (X)$ denote the variety of its $s - 1$ secant…

math.AG2007★ 1 cited

An invariant regarding Waring's problem for cubic polynomials

Giorgio Ottaviani

We compute the equation of the 7-secant variety to the Veronese variety (P^4,O(3)), its degree is 15. This is the last missing invariant in the Alexander-Hirschowitz classification…

math.AG2007★ 6 cited

On the Alexander-Hirschowitz Theorem

Maria Chiara Brambilla, Giorgio Ottaviani

The Alexander-Hirschowitz theorem says that a general collection of $k$ double points in $P^{n}$ imposes independent conditions on homogeneous polynomials of degree $d$ with a…

math.AG2004★ 2 cited

Resolutions of Segre embeddings of projective spaces of any dimension

Elena Rubei

This paper deals with syzygies of Segre embeddings. Let d >=3 and n_1, ..., n_d nonzero natural numbers. We prove that O(1,...., 1) on the product of P^{n_1}, ...,P^{n_d} satisfies…

math.AG2004★ 1 cited

Quivers and the cohomology of homogeneous vector bundles

Giorgio Ottaviani, Elena Rubei

We describe the cohomology groups of a homogeneous vector bundle $E$ on any Hermitian symmetric variety $X = G / P$ of ADE type as the cohomology of a complex explicitly described. The…

math.AG2003★ 3 cited

A result on resolutions of Veronese embeddings

Elena Rubei

This paper deals with syzygies of the ideals of the Veronese embeddings. We prove that O(3) on P^n satisfies Property N_4 for every n. Besides we prove that O(d) on P^n satisfies N…