Applications of researches on automorhisms group of K3 surfaces to the curve theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400039
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: Watanabe Kenta 大阪大学, 理学(系)研究科(研究院), 研究員 (70582683)
• Research Collaborator: KOMEDA JIRYO 神奈川工科大学, 公私立大学の部局等, 教授 (90162065)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: K3 曲面 / 代数曲線 / Weierstrass 半群 / Lazarsfeld-Mukai 束 / ACM 束

Outline of Final Research Achievements

In our research, we gave a concrete description and a classification of line bundles on a curve on a K3 surface which compute the Clifford index of it, by using Nikulin's concrete description of the set of fixed points of a non-symplectic involution on a K3 surface. On the other hand, we have characterized a sufficient condition for a double covering of a plane curve to be contained by a K3 surface, by using the computation of Weierstrass semigroups of ramification points on it. Moreover, later in the period, we have constructed an interesting example of an indecomposable stable vector bundle on a K3 surface in the point of view of the Brill-Noether theory of curves on regular surfaces.

Free Research Field

代数幾何学