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1. CJM Online first

Pan, Ivan Edgardo; Simis, Aron
 Cremona Maps of de JonquiÃ¨res Type This paper is concerned with suitable generalizations of a plane de JonquiÃ¨res map to higher dimensional space \$\mathbb{P}^n\$ with \$n\geq 3\$. For each given point of \$\mathbb{P}^n\$ there is a subgroup of the entire Cremona group of dimension \$n\$ consisting of such maps. One studies both geometric and group-theoretical properties of this notion. In the case where \$n=3\$ one describes an explicit set of generators of the group and gives a homological characterization of a basic subgroup thereof. Keywords:Cremona map, de JonquiÃ¨res map, Cremona group, minimal free resolutionCategories:14E05, 13D02, 13H10, 14E07, 14M05, 14M25

2. CJM 2010 (vol 62 pp. 1201)

Alzati, Alberto; Besana, Gian Mario
 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 surfacesCategories:14E05, 14J30

3. CJM 2000 (vol 52 pp. 1018)

Reichstein, Zinovy; Youssin, Boris
 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

4. CJM 1997 (vol 49 pp. 675)

de Cataldo, Mark Andrea A.
 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