### Abstract

Let X be a projective surface and let L be an ample line bundle on X. The global Seshadri constant ε(L) of L is defined as the infimum of Seshadri constants ε(L,x) as x∈X varies. It is an interesting question to ask if ε(L) is a rational number for any pair (X,L). We study this question when X is a blow up of P^{2} at r≥0 very general points and L is an ample line bundle on X. For each r we define a submaximality threshold which governs the rationality or irrationality of ε(L). We state a conjecture which strengthens the SHGH Conjecture and assuming that this conjecture is true we determine the submaximality threshold.

Original language | English (US) |
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Article number | 106345 |

Journal | Journal of Pure and Applied Algebra |

Volume | 224 |

Issue number | 8 |

DOIs | |

Publication status | Accepted/In press - Jan 1 2020 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

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*Journal of Pure and Applied Algebra*,

*224*(8), [106345]. https://doi.org/10.1016/j.jpaa.2020.106345