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Search: MSC category 14J40 ( $n$-folds ($n>4$) )

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1. CMB 2011 (vol 55 pp. 799)

Novelli, Carla; Occhetta, Gianluca
Manifolds Covered by Lines and Extremal Rays
Let $X$ be a smooth complex projective variety, and let $H \in \operatorname{Pic}(X)$ be an ample line bundle. Assume that $X$ is covered by rational curves with degree one with respect to $H$ and with anticanonical degree greater than or equal to $(\dim X -1)/2$. We prove that there is a covering family of such curves whose numerical class spans an extremal ray in the cone of curves $\operatorname{NE}(X)$.

Keywords:rational curves, extremal rays
Categories:14J40, 14E30, 14C99

2. CMB 2006 (vol 49 pp. 270)

Occhetta, Gianluca
A Characterization of Products of Projective Spaces
We give a characterization of products of projective spaces using unsplit covering families of rational curves.

Keywords:Rational curves, Fano varieties
Categories:14J40, 14J45

3. CMB 2001 (vol 44 pp. 452)

Ishihara, Hironobu
Some Adjunction Properties of Ample Vector Bundles
Let $\ce$ be an ample vector bundle of rank $r$ on a projective variety $X$ with only log-terminal singularities. We consider the nefness of adjoint divisors $K_X + (t-r) \det \ce$ when $t \ge \dim X$ and $t>r$. As an application, we classify pairs $(X,\ce)$ with $c_r$-sectional genus zero.

Keywords:ample vector bundle, adjunction, sectional genus
Categories:14J60, 14C20, 14F05, 14J40

4. CMB 1999 (vol 42 pp. 209)

Lanteri, Antonio; Maeda, Hidetoshi
Ample Vector Bundles of Curve Genus One
We investigate the pairs $(X,\cE)$ consisting of a smooth complex projective variety $X$ of dimension $n$ and an ample vector bundle $\cE$ of rank $n-1$ on $X$ such that $\cE$ has a section whose zero locus is a smooth elliptic curve.

Categories:14J60, 14F05, 14J40

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