莫里锥边界上的四角锥，适用于非常一般的平面吹胀

IF 0.7 2区数学 Q2 MATHEMATICS

Collectanea Mathematica Pub Date : 2024-06-18 DOI:10.1007/s13348-024-00447-7

Ciro Ciliberto, Rick Miranda, Joaquim Roé

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引用次数: 0

摘要

在本文中，我们证明了在8维有理球面上，在平面炸开的莫里锥的边界上存在着在\(\ge 13\) 非常一般的点上的锥。这为德费耐克斯的强((△\)-猜想提供了证据，众所周知这意味着永田猜想。这也意味着存在 Ciliberto 等人（Clay Math Proc 18:185-203, 2013）中定义的众多好射线和奇妙射线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Quadric cones on the boundary of the Mori cone for very general blowups of the plane

In this paper we show the existence of cones over a 8-dimensional rational sphere at the boundary of the Mori cone of the blow-up of the plane at \(s\ge 13\) very general points. This gives evidence for De Fernex’s strong \(\Delta \)-conjecture, which is known to imply Nagata’s conjecture. This also implies the existence of a multitude of good and wonderful rays as defined in Ciliberto et al. (Clay Math Proc 18:185–203, 2013).

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来源期刊

Collectanea Mathematica 数学-数学

CiteScore

2.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.