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Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.

Maria Virginia Catalisano, Anthony V. Geramita, Alessandro Gimigliano (2007)

Collectanea Mathematica

In this paper we compute the dimension of all the sth higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 × P1 × P1 in the projective space PN via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Yd has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.

Sieve methods for varieties over finite fields and arithmetic schemes

Bjorn Poonen (2007)

Journal de Théorie des Nombres de Bordeaux

Classical sieve methods of analytic number theory have recently been adapted to a geometric setting. In the new setting, the primes are replaced by the closed points of a variety over a finite field or more generally of a scheme of finite type over ℤ . We will present the method and some of the surprising results that have been proved using it. For instance, the probability that a plane curve over 𝔽 2 is smooth is asymptotically 21 / 64 as its degree tends to infinity. Much of this paper is an exposition...

Singularities on complete algebraic varieties

Fedor Bogomolov, Paolo Cascini, Bruno Oliveira (2006)

Open Mathematics

We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.

Some defective secant varieties to osculating varieties of Veronese surfaces.

Alessandra Bernardi, Maria Virginia Catalisano (2006)

Collectanea Mathematica

We consider the k-osculating varietiesOk,d to the Veronese d?uple embeddings of P2. By studying the Hilbert function of certain zero-dimensional schemes Y ⊂ P2, we find the dimension of Osk,d, the (s?1)th secant varieties of Ok,d, for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.

Some topological conditions for projective algebraic manifolds with degenerate dual varieties: connections with 𝐏 -bundles

Antonio Lanteri, Daniele Struppa (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si illustrano alcune relazioni tra le varietà proiettive complesse con duale degenere, le varietà la cui topologia si riflette in quella della sezione iperpiana in misura maggiore dell'ordinario e le varietà fibrate in spazi lineari su di una curva.

Special effect varieties in higher dimension.

Cristiano Bocci (2005)

Collectanea Mathematica

Here we introduce the concept of special effect varieties in higher dimension and we generalize to Pn, n ≥ 3, the two conjectures given in [2] for the planar case. Finally, we propose some examples on the product of projective spaces and we show how these results fit with the ones of Catalisano, Geramita and Gimigliano.

Stability of pencils of plane quartic curves

Edoardo Ballico, Paolo Oliverio (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota si danno dei criteri per la stabilità di fasci di quartiche piane.

Currently displaying 221 – 240 of 315