Monomial ideals with a prescribed Waldschmidt constant

Abstract

Let I be a monomial ideal in R=K[x_1,x_2,..,x_n], a polynomial ring over a field K. The Waldschmidt constant of I is an asymptotic invariant of I. The Waldschmidt constant manifests in many ways in commutative algebra and algebraic geometry, and is related to open problems such as the ideal containment problem and Nagata's conjecture. For a monomial ideal, the computation of its Waldschmidt constant reduces to solving a linear optimization problem. This thesis shows how to construct a monomial ideal with Waldschmidt constant equal to any rational number greater than or equal to 1. The family of monomial ideals investigated are intersections of powers of prime monomial ideals (in Chapter 3) and square-free principal Borel ideals (in Chapter 4).