关于某些非正则曲面上 Ulrich 向量丛的存在性
代数几何
2020-07-24 v5
摘要
我们证明了在具有极大 Albanese 维数或非正则性为 1 的曲面上，在多种嵌入下存在秩为 2 的 Ulrich 向量丛。特别地，我们得到了一般型非正则曲面上 Ulrich 向量丛的首批已知实例。另一个推论是，对于任意满足 或 且其极小模型秩为 1 的曲面，都存在一个简单的秩为 2 的 Ulrich 向量丛。
引用
@article{arxiv.1812.10195,
title = {On the existence of Ulrich vector bundles on some irregular surfaces},
author = {Angelo Felice Lopez},
journal= {arXiv preprint arXiv:1812.10195},
year = {2020}
}
备注
9 pages; v2: removed one unnecessary hypothesis in Theorem 1 and specified the surfaces for which the theorem applies; slightly rewritten; added several new references; v3: added a few references to extend to characteristic 0; v4: added Cor.1; v5: reorganized the proof of Lemma 3.1 into several claims