On the height constant for curves of genus two, II
Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P n with one point as support and with high regularity index.
If is a complex surface, one has for each the Hilbert scheme , which is a desingularization of the symmetric product . Here we construct more generally a differentiable variety endowed with a stable almost complex structure, for every almost complex fourfold . is a desingularization of the symmetric product .
We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.
We describe the polarised Hodge structure on the symmetric powers of a smooth projective curve.
We study, in certain cases, the notions of finiteness and stability of the set of associated primes and vanishing of the homogeneous pieces of graded generalized local cohomology modules.