Nonabelian Jacobian of smooth projective surfaces-a survey

作     者：REIDER Igor 

作者机构：Département de Mathématiquesl'Université d'Angers2 Boulevard Lavoisier49045 Angers Cedex 01France 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第1期

页      面：1-42页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Jacobian Hilbert scheme vector bundle 

摘      要：The nonabelian Jacobian J(X;L,d) of a smooth projective surface X is inspired by the classical theory of Jacobian of *** is built as a natural scheme interpolating between the Hilbert scheme X [d] of subschemes of length d of X and the stack M X(2,L,d) of torsion free sheaves of rank 2 on X having the determinant OX(L) and the second Chern class(= number) *** relates to such influential ideas as variations of Hodge structures,period maps,nonabelian Hodge theory,Homological mirror symmetry,perverse sheaves,geometric Langlands *** relations manifest themselves by the appearance of the following structures on J(X;L,d):1) a sheaf of reductive Lie algebras;2)(singular) Fano toric varieties whose hyperplane sections are(singular) Calabi-Yau varieties;3) trivalent *** is an expository paper giving an account of most of the main properties of J(X;L,d) uncovered in Reider 2006 and ArXiv:1103.4794v1.