The F-conjecture for divisors on \mathcal{X}_{n+2,}
The F-conjecture for divisors on \mathcal{X}_{n+2,}
Let be the indexing set used in the source, and let be the corresponding space. For a divisor of the form given in the source, define the intersection expressions and for partitions of . The divisor is F-nef when
for every partition and , respectively. The F-conjecture. Such a divisor is nef if and only if these F-nef inequalities hold.
This is the specialization of the F-conjecture to the stated blow-up model and translates nonnegative intersection with the relevant F-curves into explicit inequalities. The general F-conjecture is not known in full.
Sources & referencesView supporting material
Primary source
Olivia Dumitrescu and Elisa Postinghel, “Positivity of divisors on blown-up projective spaces, I”, arXiv:1506.04726 (2017).
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