Rationality of Seshadri constants on general blow ups of P2

Łucja Farnik, Krishna Hanumanthu, Jack Huizenga, David Schmitz, Tomasz Szemberg

Research output: Contribution to journalArticle

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 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.

Original languageEnglish (US)
Article number106345
JournalJournal of Pure and Applied Algebra
Volume224
Issue number8
DOIs
Publication statusAccepted/In press - Jan 1 2020

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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