A simplicial approach to effective divisors in (M)over-bar(0,n)
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2017-02
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Journal Article
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yes
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Abstract
We study the Cox ring and monoid of effective divisor classes of M¯¯¯¯0,n≅BlPn−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.
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2017 (2)
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529 - 565
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Oxford University Press
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spaces
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It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
Funding
138071 - Algebraic group actions and boundaries, with applications (SNF)