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3-dimensional sundials

Enrico Carlini, Maria Catalisano, Anthony Geramita (2011)

Open Mathematics

R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).

3-folds of general type with K 3 = 4 p g - 14

Paola Supino (1999)

Bollettino dell'Unione Matematica Italiana

In questo lavoro vengono costruite famiglie di 3-folds algebriche e non singolari X di tipo generale tali che l'invariante K X 3 sia il minimo possibile rispetto al genere geometrico p g , quando si suppone che il morfismo canonico sia birazionale. Per tali 3-folds vale la relazione lineare K X 3 = 4 p g - 14 inoltre l'immagine del morfismo canonico é una varietà di Castelnuovo di P p g - 1 .

A 4₃ configuration of lines and conics in ℙ⁵

Tomasz Szemberg (1994)

Annales Polonici Mathematici

Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.

A converse to the Andreotti-Grauert theorem

Jean-Pierre Demailly (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

The goal of this paper is to show that there are strong relations between certain Monge-Ampère integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of holomorphic line bundles. Especially, we prove that these relations hold without restriction for projective surfaces, and in the special case of the volume, i.e. of asymptotic 0 -cohomology, for all projective manifolds. These results can be seen as a partial converse to the Andreotti-Grauert...

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