Very general monomial valuations of P2 and a Nagata type conjecture

被引：6

作者：

Dumnicki, Marcin ^{[1
]}

Harbourne, Brian ^{[2
]}

Kueronya, Alex ^{[3
]}

Roe, Joaquim ^{[4
]}

Szemberg, Tomasz ^{[5
]}

机构：

[1] Jagiellonian Univ, Dept Math, PL-30348 Krakow, Poland

[2] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[3] Goethe Univ Frankfurt, Inst Math FB12, Robert Mayer Str 6-8, D-60325 Frankfurt, Germany

[4] Univ Autonoma Barcelona, Dept Matemat, Fac Ciencies, C1-346, Bellaterra 08193, Barcelona, Spain

[5] Pedag Univ Cracow, Dept Math, Podchorazych 2, PL-30084 Krakow, Poland

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2017年 / 25卷 / 01期

关键词：

Nagata Conjecture; SHGH Conjecture; Seshadri constants; monomial valuations; anticanonical divisor; RATIONAL SURFACES; DIMENSIONS; DIVISORS; CURVES; IDEALS;

D O I：

10.4310/CAG.2017.v25.n1.a4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that multi-point Seshadri constants for a small number t of points in the projective plane are submaximal. It is predicted by the Nagata conjecture that their values are maximal for t >= 9 points. Tackling the problem in the language of valuations one can make sense of t points for any real t >= 1. We show somewhat surprisingly that a Nagata-type conjecture should be valid for t >= 8 + 1/36 points and we compute explicitly all Seshadri constants (expressed here as the asymptotic maximal vanishing element) for t >= 7 + 1/9. In the range 7 + 1/9 <= t <= 8 + 1/36 we are able to compute some sporadic values.

引用

页码：125 / 161

页数：37

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