Given s distinct points P1,…, Ps in the projective plane and s positive integers m1,…, ms, let S_t be the linear system of plane curves of degree t through Pi with multiplicity at least mi (1 ⩽ i ⩽ s) and let Z be the subscheme of fat points m1P1+...+msPs. In this paper, under the condition that the Pi lie on a nonsingular conic, we answer the following questions: what is the dimension of S_t; what is the Hilbert function of Z; what about a minimal free resolution of the ideal I_Z of the scheme Z.
"Fat'' points on a conic
CATALISANO, MARIA VIRGINIA
1991-01-01
Abstract
Given s distinct points P1,…, Ps in the projective plane and s positive integers m1,…, ms, let S_t be the linear system of plane curves of degree t through Pi with multiplicity at least mi (1 ⩽ i ⩽ s) and let Z be the subscheme of fat points m1P1+...+msPs. In this paper, under the condition that the Pi lie on a nonsingular conic, we answer the following questions: what is the dimension of S_t; what is the Hilbert function of Z; what about a minimal free resolution of the ideal I_Z of the scheme Z.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
