Balanced complexes and effective divisors on

Abstract

Doran, Giansiracusa, and Jensen showed a bijection between homogeneous elements in the Cox ring of not divisible by any exceptional divisor section, and weighted pure-dimensional simplicial complexes satisfying a zero-tension condition. Motivated by the study of the monoid of effective divisors, the pseudoeffective cone and the Cox ring of we point out a simplification of the zero-tension condition and study the space of balanced complexes. We give examples of irreducible elements in the monoid of effective divisors of for large n. In the case of we classify all such irreducible elements arising from nonsingular complexes and give an example of how irreducibility can be shown in the singular case.Communicated by Lawrence Ein