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On the Hilbert scheme of points of an almost complex fourfold

Claire Voisin (2000)

Annales de l'institut Fourier

If S is a complex surface, one has for each k the Hilbert scheme Hilb k ( S ) , which is a desingularization of the symmetric product S ( k ) . Here we construct more generally a differentiable variety Hilb k ( X ) endowed with a stable almost complex structure, for every almost complex fourfold X . Hilb k ( X ) is a desingularization of the symmetric product X ( k ) .

On the Hodge cycles of Prym varieties

Indranil Biswas (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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.

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