A Tropical View on Landau-Ginzburg Models

作     者：Michael CARL Max PUMPERLA Bernd SIEBERT Michael CARL;Max PUMPERLA;Bernd SIEBERT

作者机构：Alfred-Delp-Str.273430 AalenGermany IU Internationale HochschuleJuri-Gagarin-Ring 15299084 ErfurtGermany AnyscaleInc.2080 Addison St Ste 7BerkeleyCA 94704USA Department of MathematicsThe Univ.of Texas at Austin2515 SpeedwayAustinTX 78712USA 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第1期

页      面：329-382页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the Studienstiftung des deutschen Volkes supported by NSF grant DMS-1903437 

主　　题：Landau-Ginzburg model mirror symmetry tropical disk broken line wall structure scattering diagram Gross-Siebert program del Pezzo surface toric degeneration 

摘      要：This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since *** point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines,previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for P2.A ma jor insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror *** obtain proper superpotentials which agree on an open part with those classically known for toric *** include mirror LG models for non-singular and singular del Pezzo surfaces,Hirzebruch surfaces and some Fano threefolds.