Displaying 21 – 40 of 78

Showing per page

Generalized Mukai conjecture for special Fano varieties

Marco Andreatta, Elena Chierici, Gianluca Occhetta (2004)

Open Mathematics

Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.

Geometry of the genus 9 Fano 4-folds

Frédéric Han (2010)

Annales de l’institut Fourier

We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.

Halphen pencils on weighted Fano threefold hypersurfaces

Ivan Cheltsov, Jihun Park (2009)

Open Mathematics

On a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.

Moduli of certain Fano 4-folds.

Walter L. Baily Jr. (2001)

Revista Matemática Iberoamericana

In this brief note we give a proof that a certain family of Fano 4-folds, described below, is complex (locally) complete and effectively parametrized in the sense of Kodaira-Spencer [Ko-Sp].

Currently displaying 21 – 40 of 78