A simplicial approach to effective divisors in (M)over-bar(0,n)

作者：Doran Brent; Giansiracusa Noah; Jensen David

来源：International Mathematics Research Notices, 2017, 2017(2): 529-565.

DOI：10.1093/imrn/rnw038

We study the Cox ring and monoid of effective divisor classes of (M) over bar (0, n) congruent to Bl Pn-3, over a ring R. We provide a bijection between elements of the Cox ring, not divisible by any exceptional divisor section, and pure- dimensional singular simplicial complexes on {1,..., n - 1} with weights in R \ {0} satisfying a zero- tension condition. This leads to a combinatorial criterion, satisfied by many triangulations of closed manifolds, for a divisor class to be among the minimal generators for the effective monoid. For classes obtained as the strict transform of quadrics, we present a complete classification of minimal generators, generalizing to all n the well- known Keel- Vermeire classes for n = 6. We use this classification to construct new divisors with interesting properties for all n >= 7.

• 出版日期2017-2