Expand all Collapse all | Results 1 - 8 of 8 |
1. CMB 2012 (vol 57 pp. 303)
Octonion Algebras over Rings are not Determined by their Norms Answering a question of H. Petersson, we provide
a class of examples of pair of octonion algebras over a ring having isometric
norms.
Keywords:octonion algebras, torsors, descent Categories:14L24, 20G41 |
2. CMB 2012 (vol 57 pp. 97)
Rationality and the Jordan-Gatti-Viniberghi decomposition We verify
our earlier conjecture
and use it to prove that the
semisimple parts of the rational Jordan-Kac-Vinberg decompositions of
a rational vector all lie in a single rational orbit.
Keywords:reductive group, $G$-module, Jordan decomposition, orbit closure, rationality Categories:20G15, 14L24 |
3. CMB 2006 (vol 49 pp. 592)
Group Actions, Cyclic Coverings and Families of K3-Surfaces In this paper we describe six pencils of $K3$-surfaces which have
large Picard number ($\rho=19,20$) and each contains precisely five
special fibers: four have A-D-E singularities and one is
non-reduced. In particular, we characterize these surfaces as cyclic
coverings of some $K3$-surfaces described in a recent paper by Barth
and the author.
In many cases, using
3-divisible sets, resp., 2-divisible sets, of rational curves and
lattice theory, we describe explicitly the Picard lattices.
Categories:14J28, 14L30, 14E20, 14C22 |
4. CMB 2004 (vol 47 pp. 22)
A Note on the Height of the Formal Brauer Group of a $K3$ Surface Using weighted Delsarte surfaces, we give examples of $K3$ surfaces
in positive characteristic whose formal Brauer groups have height
equal to $5$, $8$ or $9$. These are among the four values of the
height left open in the article of Yui \cite{Y}.
Keywords:formal Brauer groups, $K3$ surfaces in positive, characteristic, weighted Delsarte surfaces Categories:14L05, 14J28 |
5. CMB 2003 (vol 46 pp. 204)
Rationality and Orbit Closures Suppose we are given a finite-dimensional vector space $V$ equipped
with an $F$-rational action of a linearly algebraic group $G$, with
$F$ a characteristic zero field. We conjecture the following: to each
vector $v\in V(F)$ there corresponds a canonical $G(F)$-orbit of
semisimple vectors of $V$. In the case of the adjoint action, this
orbit is the $G(F)$-orbit of the semisimple part of $v$, so this
conjecture can be considered a generalization of the Jordan
decomposition. We prove some cases of the conjecture.
Categories:14L24, 20G15 |
6. CMB 2003 (vol 46 pp. 140)
An Explicit Cell Decomposition of the Wonderful Compactification of a Semisimple Algebraic Group We determine an explicit cell decomposition of the wonderful
compactification of a semi\-simple algebraic group. To do this we first
identify the $B\times B$-orbits using the generalized Bruhat
decomposition of a reductive monoid. From there we show how each cell
is made up from $B\times B$-orbits.
Categories:14L30, 14M17, 20M17 |
7. CMB 2002 (vol 45 pp. 686)
An Aspect of Icosahedral Symmetry We embed the moduli space $Q$ of 5 points on the projective line
$S_5$-equivariantly into $\mathbb{P} (V)$, where $V$ is the
6-dimensional irreducible module of the symmetric group $S_5$. This
module splits with respect to the icosahedral group $A_5$ into the two
standard 3-dimensional representations. The resulting linear
projections of $Q$ relate the action of $A_5$ on $Q$ to those on the
regular icosahedron.
Categories:14L24, 20B25 |
8. CMB 2001 (vol 44 pp. 491)
Resolution of Singularities of Null Cones We give canonical resolutions of singularities of several cone
varieties arising from invariant theory. We establish a connection
between our resolutions and resolutions of singularities of closure of
conjugacy classes in classical Lie algebras.
Categories:14L35, 22G |