Semisimple group actions on the three dimensional affine space are linear.
In the present paper, we give a first general construction of compactified moduli spaces for semistable -bundles on an irreducible complex projective curve with exactly one node, where is a semisimple linear algebraic group over the complex numbers.
For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in is quasi-projective.
In questa nota si danno dei criteri per la stabilità di fasci di quartiche piane.
On décrit l’algèbre des invariants de l’action naturelle du groupe sur les pinceaux de formes quintiques binaires.