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For a smooth complex projective variety, the rank $ρ$ of the Néron-Severi group is bounded by the Hodge number $h^{1, 1}$ . Varieties with $ρ = h^{1, 1}$ have interesting properties, but are rather sparse, particularly in dimension $2$ . We discuss in this note a number of examples, in particular those constructed from curves with special Jacobians.

Some topological conditions for projective algebraic manifolds with degenerate dual varieties: connections with $\mathbf{P}$ -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.

Sous-groupes analytiques de variétés de groupe et théorème de Brumer

Daniel Bertrand (1979/1981)

Groupe de travail d'analyse ultramétrique

Spaces of geometrically generic configurations

Yoel Feler (2008)

Journal of the European Mathematical Society

Let $X$ denote either ${ℂℙ}^{m}$ or $ℂ^{m}$ . We study certain analytic properties of the space $ℰ^{n} (X, g p)$ of ordered geometrically generic $n$ -point configurations in $X$ . This space consists of all $q = (q_{1}, \dots, q_{n}) \in X^{n}$ such that no $m + 1$ of the points $q_{1}, \dots, q_{n}$ belong to a hyperplane in $X$ . In particular, we show that for a big enough $n$ any holomorphic map $f : ℰ^{n} ({ℂℙ}^{m}, g p) \to ℰ^{n} ({ℂℙ}^{m}, g p)$ commuting with the natural action of the symmetric group $𝐒 (n)$ in $ℰ^{n} ({ℂℙ}^{m}, g p)$ is of the form $f (q) = τ (q) q = (τ (q) q_{1}, \dots, τ (q) q_{n})$ , $q \in ℰ^{n} ({ℂℙ}^{m}, g p)$ , where $τ : ℰ^{n} ({ℂℙ}^{m}, g p) \to 𝐏𝐒𝐋 (m + 1, ℂ)$ is an $𝐒 (n)$ -invariant holomorphic map. A similar result holds true for mappings of the configuration space $ℰ^{n} (ℂ^{m}, g p)$ .

Special divisors on curves on a K3 surface.

M., Lazarsfeld, R. Green (1987)

Inventiones mathematicae

Special Kähler metrics on complex line bundles and the geometry of $K 3$ -surfaces.

Bazajkin, Ya.V. (2005)

Sibirskij Matematicheskij Zhurnal

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