On the Decomposition Group of a Nonsingular Plane Cubic by a Log Calabi-Yau Geometrical Perspective
Abstract
Abstract This paper aims to study the decomposition group of a nonsingular plane cubic under the light of the log Calabi-Yau geometry. Using this approach we prove that an appropriate algorithm of the Sarkisov program in dimension 2 applied to an element of this group is automatically volume preserving. From this, we deduce some properties of the (volume preserving) Sarkisov factorization of its elements. We also confirm an expectation by Blanc, Pan and Vust on the splitting property of the canonical complex of a nonsingular plane cubic. Within a similar context in dimension 3, we exhibit in detail an interesting counterexample for a possible generalization of a theorem by Pan in which there exists a Sarkisov factorization obtained algorithmically that is not volume preserving.
Fields of Study & Subjects
Mathematics and Applications
Advanced Topics in Algebra
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Transformation Groups
- Publisher
- Springer Science and Business Media LLC
- Volume
- 31
- Issue
- 3
- Pages
- 2627–2656
- Publication date
- 20 July 2026
- Language
- EN