A working seminar organized by Raymond Cheng and Stefan Schreieder during the fall of 2024
Rational curves, whether through their abundance or absence, provide a powerful method of measuring the complexity of algebraic varieties.
This seminar falls into three parts. In the first third, we work through the basic theory around rational curves in algebraic varieties and rational connectedness. In the second part, we look to understand recent work of Kollár and Zhiyu Tian on lifting algebraic equivalence of \(1\)-cycles to deformation equivalence, and its arithmetic consequences. The final part of the seminar will cover topics of interest proposed by participants of the seminar.
Two excellent and comprehensive references for the basic theory of rational curves on algebraic varieties include the following two books:
These works have been remixed into brief and introductory notes:
Original papers in this subject that we touch upon include:
In the second part of the seminar, we look to understand the recent work of Kollár and Zhiyu Tian:
We meet Thursdays in F107 between 14:15 and 15:45. A program may also be found here.