代数簇间的双有理变换是代数几何中的重要研究对象。本项目将研究一种特殊的双有理变换：简单双有理变换，即 K-等价的可以被一次blowing up 消解的双有理变换。本项目拟研究与简单双有理变换相关的若干问题，包括简单双有理变换的分类、简单双有理变换的导出范畴等价和某些特殊代数簇的光滑射影同态像等问题。从双有理变换的弱分解定理的角度看，简单双有理变换是一般双有理变换的组成模块，是对一般双有理变换的细化研究。通过本项目的研究，可以加深对双有理几何和有理齐性簇的理解。

Birational map between algebraic varieties is an important research topic in algebraic geometry. This project will focus on the study of a special kind of birational maps: simple birational maps, which are K-equivalent and resolved by a single blowing up. In this project, we will study several related problems, including the classification of simple birational maps, derived equivalence of simple birational maps and smooth projective images of some special varieties. By the weak factorization theorem of birtional maps between algebraic varieties, simple birational map is an important step to construct general birational maps. We expect a better understanding of birational geometry and rational homogeneous varieties by researching this project.