On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold.
Let be a projective Frobenius split variety with a fixed Frobenius splitting . In this paper we give a sharp uniform bound on the number of subvarieties of which are compatibly Frobenius split with . Similarly, we give a bound on the number of prime -ideals of an -finite -pure local ring. Finally, we also give a bound on the number of log canonical centers of a log canonical pair. This final variant extends a special case of a result of Helmke.
Let be an integral projective curve with . For all positive integers , let be the set of all with and spanned. Here we prove that if , then except in a few cases (essentially if is a double covering).
Sia una curva proeittiva e lissa, generali nel senso di Brill-Noether, indichiamo con l'insieme algebrico di quadrici di rango contenendo a . In questo lavoro noi descriviamo birazionalmente i componenti irriducibile di .