TY - JOUR

T1 - Rationality of Seshadri constants on general blow ups of P2

AU - Farnik, Łucja

AU - Hanumanthu, Krishna

AU - Huizenga, Jack

AU - Schmitz, David

AU - Szemberg, Tomasz

N1 - Funding Information:
Acknowledgments . We thank the Mathematisches Forschungsinstitut Oberwolfach for hosting the Mini-Workshop Asymptotic Invariants of Homogeneous Ideals during September 30 – October 6, 2018, where most of this work was done. The research stay of the second author was partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach and he is grateful to them. We would also like to thank the referee, whose comments helped improve the exposition of the paper.
Funding Information:
?F was partially supported by the National Science Centre, Poland, grant 2018/28/C/ST1/00339. KH was partially supported by a grant from Infosys Foundation and by DST SERB MATRICS grant MTR/2017/000243. JH was partially supported by the NSA Young Investigator Grant H98230-16-1-0306 and NSF FRG grant DMS 1664303. DS was partially supported by DFG grant PE 305/13-1. TS was partially supported by the National Science Centre Poland, grant 2018/30/M/ST1/00148.Acknowledgments. We thank the Mathematisches Forschungsinstitut Oberwolfach for hosting the Mini-Workshop Asymptotic Invariants of Homogeneous Ideals during September 30 ? October 6, 2018, where most of this work was done. The research stay of the second author was partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach and he is grateful to them. We would also like to thank the referee, whose comments helped improve the exposition of the paper.
Funding Information:
ŁF was partially supported by the National Science Centre , Poland, grant 2018/28/C/ST1/00339 . KH was partially supported by a grant from Infosys Foundation and by DST SERB MATRICS grant MTR/2017/000243 . JH was partially supported by the NSA Young Investigator Grant H98230-16-1-0306 and NSF FRG grant DMS 1664303 . DS was partially supported by DFG grant PE 305/13-1 . TS was partially supported by the National Science Centre Poland, grant 2018/30/M/ST1/00148 .
Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/8

Y1 - 2020/8

N2 - 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 P2 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.

AB - 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 P2 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.

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U2 - 10.1016/j.jpaa.2020.106345

DO - 10.1016/j.jpaa.2020.106345

M3 - Article

AN - SCOPUS:85079280709

VL - 224

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 8

M1 - 106345

ER -