Some Results on Spanned Vector Bundles of Corank 0

IF 1 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2026-06-05 Epub Date: 2026-04-29 DOI:10.1002/mana.70153

Antonio Lanteri, Andrew J. Sommese

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引用次数: 0

Abstract

A class $C$ of vector bundles $E$ of rank $N$ on an $N$ -dimensional complex projective variety $X$ , spanned by global sections, with positive top Chern class and ample determinant is investigated. The standard relation between Chern and Segre polynomials allows us to decide about the bigness of a bundle closely related to $E$ . The size $σ (X, E)$ , an integer measuring the deviation of $E$ from bigness, is introduced and studied. The structure of $C$ , in connection with the behavior of the size, yields a useful tool to produce several examples. Among them the pair $(P^{N}, T_{P^{N}} (- 1))$ emerges, of which two characterizations are provided in terms of $σ (X, E)$ and in terms of the degree of curves representing $c_{N - 1}$ with respect to the determinant.

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Corank 0的张成向量束的一些结果

研究了秩为N$ N$的N$ N维复射影变簇X$ X$上的一类C ${\mathcal {C}}$的向量束E ${\mathcal {E}}$，由全局截面张成，具有正的顶陈氏类和充足行列式。Chern多项式和Segre多项式之间的标准关系允许我们决定与E ${\mathcal {E}}$密切相关的束的大小。引入并研究了度量E ${\mathcal {E}}$偏离大的整数σ (X， E)$ \sigma (X,{\mathcal {E}}$)$的大小。C ${\mathcal {C}}$的结构与大小的行为有关，产生了一个有用的工具来生成几个示例。其中一对(P N，T P N(−1))$ (\mathbb {P}^N, T_{\mathbb {P}^N}(-1))$出现，给出了两种用σ (X)表示的表征，E)$ \sigma (X,{\mathcal {E}})$以及表示c N−1的曲线的度$c_{N-1}$关于行列式。

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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