Seshadri constant conjecture for many points on a surface

Let XX be a smooth projective surface and let LL be a nef divisor on XX. Let ϵ(n;X,L)\epsilon(n;X,L) denote the relevant multipoint Seshadri constant for nn points. Seshadri constant conjecture. There is a positive integer n0n_0 such that

ϵ(n;X,L)=L2/n\epsilon(n;X,L)=\sqrt{L^2/n}

for every nn0n\ge n_0. This generalizes the expected value for very general points on the plane and concerns the asymptotic geometry of nef divisors and multipoint Seshadri constants; no resolution is given in the source.

Sources & referencesView supporting material

Primary source

Joaquim Roé and Paola Supino, “Nagata type statements”, arXiv:1707.00583 (2017).

Additional references

2 papers in this index state this conjecture (2006–2017). The statement above is taken from the most recent of them; the others are arXiv:math/0608224.

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