Hirzebruch曲面膨胀的Seshadri常数

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-11-14 DOI:10.1002/mana.202400018

Krishna Hanumanthu, Cyril J. Jacob, B. N. Suhas, Amit Kumar Singh

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引用次数: 0

摘要

设e,r≥0$ e,r \ge 0$为整数，设F e:= P(或p1⊕或p1)−e))$ \mathbb {F}_e: = \mathbb {P}(\mathcal {O}_{mathbb {P}^1} \oplus \mathcal {O}_{mathbb {P}^1}(-e))$表示不变量e$ e$的Hirzebruch曲面。我们计算了当r≤e−1$ r \le e-1$时，F e$ \mathbb {F}_e$的r$ r$ -点膨胀的任意点和在一个非常一般的点r=e$ r=e$或r=e+1$ r=e+1$我们还讨论了关于F e$ \mathbb {F}_e$在r$ r$非常一般点爆破的线性曲线系统的几个猜想。

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Seshadri constants on blow-ups of Hirzebruch surfaces

Let $e, r \geq 0$ be integers and let $F_{e} : = P (O_{P^{1}} \oplus O_{P^{1}} (- e))$ denote the Hirzebruch surface with invariant $e$ . We compute the Seshadri constants of an ample line bundle at an arbitrary point of the $r$ -point blow-up of $F_{e}$ when $r \leq e - 1$ and at a very general point when $r = e$ or $r = e + 1$ . We also discuss several conjectures on linear systems of curves on the blow-up of $F_{e}$ at $r$ very general points.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index