Given a linear system in P^n with assigned multiple general points, we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear system, which takes into account the contribution of the linear base locus, and thus to introduce the notion of linear speciality. We investigate such a notion, giving sufficient conditions for a linear system to be linearly non-special for an arbitrary number of points and necessary conditions for a small number of points.
On a notion of speciality of linear systems in P^n / Brambilla, Maria Chiara; Olivia, Dumitrescu; Elisa, Postinghel. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 367:(2015), pp. 5447-5473. [10.1090/S0002-9947-2014-06212-0]
On a notion of speciality of linear systems in P^n
BRAMBILLA, Maria Chiara;
2015-01-01
Abstract
Given a linear system in P^n with assigned multiple general points, we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear system, which takes into account the contribution of the linear base locus, and thus to introduce the notion of linear speciality. We investigate such a notion, giving sufficient conditions for a linear system to be linearly non-special for an arbitrary number of points and necessary conditions for a small number of points.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
