Balanced complexes and effective divisors on M¯0,n

Abstract

Doran, Jensen and Giansiracusa showed a bijection between homogeneous elements in the Cox ring of M 0,n 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 M 0,n , 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 M 0,n for large n. In the case of M 0,7 , we classify all such irreducible elements arising from nonsingular complexes and give an example of how irreducibility can be shown in the singular case.

Weighted persistent homology

“…The final part of this paper (Section 7) is about the generalized Bockstein spectral sequence, where we consider coefficients in an integral domain R. A potential application is in algebraic geometry where recently there has been some interest in the usage of weighted simplicial complexes [18,20] with weights in a ring R.…”