Normal bundle to curves in quadrics
We prove that a very ample special line bundle of degree on a general -gonal curve is normally generated if the degree of the base locus of its dual bundle does not exceed , where .
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting automorphism.
Given an irreducible representation of a complex simply connected semisimple algebraic group we consider the closure of the image of in . We determine for which the variety is normal and for which is smooth.
On classifie les orbites de sur l’immeuble de Bruhat-Tits de pour trois paires sphériques de groupes -adiques classiques.