1. CJM 2010 (vol 62 pp. 1201)
|Criteria for Very Ampleness of Rank Two Vector Bundles over Ruled Surfaces|
Very ampleness criteria for rank $2$ vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.
Keywords:vector bundles, very ampleness, ruled surfaces
2. CJM 2000 (vol 52 pp. 1018)
|Essential Dimensions of Algebraic Groups and a Resolution Theorem for $G$-Varieties |
Let $G$ be an algebraic group and let $X$ be a generically free $G$-variety. We show that $X$ can be transformed, by a sequence of blowups with smooth $G$-equivariant centers, into a $G$-variety $X'$ with the following property the stabilizer of every point of $X'$ is isomorphic to a semidirect product $U \sdp A$ of a unipotent group $U$ and a diagonalizable group $A$. As an application of this result, we prove new lower bounds on essential dimensions of some algebraic groups. We also show that certain polynomials in one variable cannot be simplified by a Tschirnhaus transformation.
Categories:14L30, 14E15, 14E05, 12E05, 20G10
3. CJM 1997 (vol 49 pp. 675)
|Some adjunction-theoretic properties of codimension two non-singular subvarities of quadrics |
We make precise the structure of the first two reduction morphisms associated with codimension two non-singular subvarieties of non-singular quadrics $\Q^n$, $n\geq 5$. We give a coarse classification of the same class of subvarieties when they are assumed not to be of log-general-type.}
Keywords:Adjunction Theory, classification, codimension two, conic bundles,, low codimension, non log-general-type, quadric, reduction, special, variety.
Categories:14C05, 14E05, 14E25, 14E30, 14E35, 14J10