A¹-cylinders over smooth A¹-fibered affine surfaces

於 城崎国際アートセンター(2019年10月21日-10月25日)2019年度科学研究費補助金 基盤研究(S)(課題番号15H05738, 代表 金銅誠之), 2019年度科学研究費補助金 基盤研究(S)(課題番号16H06337, 代表 高橋篤史), 2019年度科学研究費補助金 基盤研究(S)(課題番号17H06127, 代表 齋藤政彦)Date : Oct. 21, 2019 (Mon) - Oct. 25, 2019 (Fri). Venue : Kinosaki International Arts Center.Kinosaki Algebraic Geometry Symposium 2019 is partially supported by Grantin-Aid for Scientific Research (S) 15H05738, (S) 16H06337, and (S) 17H06127. Organizers: Hiraku Kawanoue (Chubu University), Takashi Kishimoto (Saitama University), Shingo Taki (Tokai University)We give a general structure theorem for affine A1-fibrations on smooth quasi-projective surfaces. As an application, we show that every smooth A1-fibered affine surface non-isomorphic to the total space of a line bundle over a smooth affine curve fails the Zariski Cancellation Problem. The present note is an expanded version of a talk given at the Kinosaki Algebraic Geometry Symposium in October 2019