1,559 research outputs found
A geometrical construction for the polynomial invariants of some reflection groups
In these notes we investigate the rings of real polynomials in four
variables, which are invariant under the action of the reflectiongroups [3,4,3]
and [3,3,5]. It is well known that they are rationally generated in degree
2,6,8,12 and 2,12,20,30. We give a different proof of this fact by giving
explicit equations for the generating polynomials.Comment: 10 page
Symmetries of order four on K3 surfaces
We study automorphisms of order four on K3 surfaces. The symplectic ones have
been first studied by Nikulin, they are known to fix six points and their
action on the K3 lattice is unique. In this paper we give a classification of
the purely non-symplectic automorphisms by relating the structure of their
fixed locus to their action on cohomology, in the following cases: the fixed
locus contains a curve of genus g>0; the fixed locus contains at least a curve
and all the curves fixed by the square of the automorphism are rational. We
give partial results in the other cases. Finally, we classify non-symplectic
automorphisms of order four with symplectic square.Comment: Final version, to appear in J. Math. Soc. Japa
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