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1. CMB 2011 (vol 55 pp. 799)
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)
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)
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)
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 |