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AFFINE CUBIC SURFACES AND RELATIVE SL(2)-CHARACTER VARIETIES OF COMPACT SURFACES
AFFINE CUBIC SURFACES RELATIVE SL(2)-CHARACTER
2015/9/29
A natural family of affine cubic surfaces arises from
SL(2)-characters of the 4-holed sphere and the 1-holed torus. The
ideal locus is a tritangent plane which is generic in the sense that
the...
Quadratic congruences on average and rational points on cubic surfaces
Quadratic congruences rational points Manin’s conjecture cubic surfaces universal torsors
2012/5/24
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.
Configuration types and cubic surfaces
Fat points free resolution cubic surface matroid Hilbert function
2012/4/16
This paper is a sequel to the paper \cite{refGH}. We relate the matroid notion of a combinatorial geometry to a generalization which we call a configuration type. Configuration types arise when one cl...
The double cover of cubic surfaces branched along their Hessian
double cover cubic surfaces branched
2011/2/23
We prove the relation between the Hodge structure of the double cover of a nonsingular cubic surface branched along its Hessian and the Hodge structure of the triple cover of P3 branched along the cub...
On the number of Mordell-Weil generators for cubic surfaces
cubic surfaces rational points Mordell-Weil problem Brauer-Manin
2011/1/19
Let S be a smooth cubic surface over a field K. It is well-known that new K-rational points maybe obtained from old ones by chord and tangent constructions.
On the Brauer-Manin obstruction for cubic surfaces
the Brauer-Manin obstruction cubic surfaces
2010/11/11
We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over $\bbQ$ such that $\Br(S)/\Br(\bbQ)$ is of order two or four. This covers the vast majority of the cases when...