关于具有弱Ulrich或初始化aCM切丛的极化曲面的分类

中文摘要 AI 辅助

最近出现了关于Ulrich丛存在的Eisenbud-Schreyer猜想的反例（参见Anghel [A1]和第三作者[Lo]）。由于弱Ulrich丛是Ulrich丛的有用推广，本文中我们分类了具有弱Ulrich切丛的光滑曲面$S\subseteq \mathbb P^N$。它们是度至少为5的Del-Pezzo曲面，并且我们分类了可能的嵌入。一个有趣的特征是出现了两个无限系列的极化，这与Ulrich情形[BMPT, LR]相当不同。我们还完成了具有初始化aCM切丛的曲面的分类，并由此得到了具有几乎Ulrich切丛的曲面的分类。

英文摘要

Counterexamples to the Eisenbud-Schreyer conjecture on the existence of Ulrich bundles have appeared recently (see Anghel [A1] and the third author [Lo]). As weakly Ulrich bundles are a useful generalization of Ulrich ones, in this paper, we classify smooth surfaces $S\subseteq \mathbb P^N$ with weakly Ulrich tangent bundle. They are Del-Pezzo surfaces of degree at least 5 and we classify the possible embeddings. An interesting feature is the appearance of two infinite series of polarizations, which is quite different from the Ulrich case [BMPT, LR]. We also achieve the classification of surfaces with initialized aCM tangent bundles and, as a consequence, of surfaces with almost Ulrich tangent bundles.

发表机构

• Chennai Mathematical Institute（金奈数学研究所）
• TED University（TED大学）
• Università di Roma Tre（罗马第三大学）

机构由 AI 辅助整理，请以论文原文为准。