We consider the Fano scheme F_k(X) of k–dimensional linear subspaces contained in a complete intersection X in projective space IP^n, of multi-degree (d_1,..., d_s). Our main result is an extension of a result of Riedl and Yang concerning Fano schemes of lines on very general hypersurfaces: we consider the case when X is a very general complete intersection and the product of the d_i's is bigger than 2 and we find conditions on n, (d_1,...,d_s) and k under which F_k(X) does not contain either rational or elliptic curves. At the end of the paper, we study the case when the product of the d_i's is 2.
Bastianelli, F., Ciliberto, C., Flamini, F., Supino, P. (2020). On Fano schemes of linear subspaces of general complete intersections. ARCHIV DER MATHEMATIK, 2020(115), 639-645 [https://doi.org/10.1007/s00013-020-01523-7].
On Fano schemes of linear subspaces of general complete intersections
Supino, P
2020-01-01
Abstract
We consider the Fano scheme F_k(X) of k–dimensional linear subspaces contained in a complete intersection X in projective space IP^n, of multi-degree (d_1,..., d_s). Our main result is an extension of a result of Riedl and Yang concerning Fano schemes of lines on very general hypersurfaces: we consider the case when X is a very general complete intersection and the product of the d_i's is bigger than 2 and we find conditions on n, (d_1,...,d_s) and k under which F_k(X) does not contain either rational or elliptic curves. At the end of the paper, we study the case when the product of the d_i's is 2.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
