A k-configuration of type (d1, . . . , ds ), where 1  d1 < · · · < ds are integers, is a set of points in P2 that has a number of algebraic and geometric properties. For example, the graded Betti numbers and Hilbert functions of all k-configurations in P2 are determined by the type (d1, . . . , ds ). However the Waldschmidt constant of a k-configuration in P2 of the same type may vary. In this paper, we find that the Waldschmidt constant of a k-configuration in P2 of type (d1, . . . , ds ) with d1 ≥ s ≥ 1 is s. Then we deal with theWaldschmidt constants of standard k-configurations inP2 of type (a), (a, b), and (a, b, c) with a ≥ 1. In particular, we prove that theWaldschmidt constant of a standard k-configuration in P2 of type (1, b, c) with c ≥ 2b+2 does not depend on c.
The Waldschmidt constant of a standard $$\Bbbk $$ k -configuration in $${\mathbb P}^2$$ P 2
Elena Guardo;
2024-01-01
Abstract
A k-configuration of type (d1, . . . , ds ), where 1 d1 < · · · < ds are integers, is a set of points in P2 that has a number of algebraic and geometric properties. For example, the graded Betti numbers and Hilbert functions of all k-configurations in P2 are determined by the type (d1, . . . , ds ). However the Waldschmidt constant of a k-configuration in P2 of the same type may vary. In this paper, we find that the Waldschmidt constant of a k-configuration in P2 of type (d1, . . . , ds ) with d1 ≥ s ≥ 1 is s. Then we deal with theWaldschmidt constants of standard k-configurations inP2 of type (a), (a, b), and (a, b, c) with a ≥ 1. In particular, we prove that theWaldschmidt constant of a standard k-configuration in P2 of type (1, b, c) with c ≥ 2b+2 does not depend on c.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.