发表机构
Università di Ferrara; Tokyo University of Science; The University of Danang - University of Science and Technology（费拉拉大学; 东京理科大学; 岘港大学-科技大學）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文对次数为4且长度为2的平面Cremona映射在射影平面自同构作用下进行分类，并计算其普通二次长度，证明该长度至多为7且分类达到上界的映射。
AI 中文摘要
根据其同调型，次数为四的平面Cremona映射被分为两类：要么是de Jonquières型，即具有一个重数为3的基点；要么不是de Jonquières型。根据Blanc和Furter给出的平面Cremona映射长度的定义，前一类映射的长度为1，而后一类映射的长度为2。本文在射影平面自同构在映射左侧和右侧的作用意义下，对次数为4且长度为2的平面Cremona映射进行分类。这一分类还使我们能够计算所有这些映射的普通二次长度。特别地，我们证明该普通二次长度至多为7，并对达到这一上界的映射进行了分类。
英文摘要
Plane Cremona maps of degree four are divided into two different classes according to their homaloidal type: either they are de Jonquières, that is, they have a base point of multiplicity 3, or they are not de Jonquières. The maps of the former class have length one, while the maps of the latter class have length two, according to the definition of length of a plane Cremona map given by Blanc and Furter. In this paper, we classify plane Cremona maps of degree four and length two, up to the action of automorphisms of the projective plane on the left-hand side and on the right-hand side of the map. This classification also allows us to compute the ordinary quadratic length of all such maps. In particular, we show that this ordinary quadratic length is at most 7 and we classify those maps which attain this upper bound.
