On the cone conjecture for log Calabi -- You mirrors of Fano 3-folds

Abstract

於 京都大学理学研究科セミナーハウス (2024年10月22日-10月25日)2024年度科学研究費補助金 基盤研究(A)(課題番号 20H00111, 代表 小木曽啓示)2024年度科学研究費補助金 基盤研究(A)(課題番号 21H04429, 代表 並河良典)Date : October 22nd - 25th, 2024Location: Kyoto University (North Campus), Science Seminar HouseJSPS KAKENHI Grant-in-Aid (A) 20H00111 (Keiji Oguiso)JSPS KAKENHI Grant-in-Aid (A) 21H04429 (Yoshinori Namikawa)Organizers: Yohsuke Matsuzawa, Yusuke Nakamura, Kazuhiko YamakiLet be a smooth projective 3-fold admitting a K3 fibration :→ ℙ¹ with -ᵧ = = *(1). We show that the pseudo-automorphism group of acts with finitely many orbits on the codimension one faces of the movable cone if ³ (, ) = 0, confirming a special case of the Kawamata-MorrisonTotaro cone conjecture. In Coates-Corti-Galkin-Kasprzyk 2016, Przyjalkowski 2018, and CheltsovPrzyjalkowski 2018, the authors construct log Calabi-Yau 3-folds with K3 fibrations satisfying the hypotheses of our theorem as the mirrors of Farro 3-folds