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[null,"1.","Record Nr.",null,"UNINA9910733710003321"]
[null,null,"Autore",null,"Reider Igor"]
[null,null,"Titolo",null,"Nonabelian Jacobian of Projective Surfaces : Geometry and Representation Theory / / by Igor Reider"]
[null,null,"Pubbl/distr/stampa",null,"Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013"]
[null,null,"ISBN",null,"3-642-35662-1"]
[null,null,"Edizione",null,"[1st ed. 2013.]"]
[null,null,"Descrizione fisica",null,"1 online resource (VIII, 227 p.)"]
[null,null,"Collana",null,"Lecture Notes in Mathematics, , 0075-8434 ; ; 2072"]
[null,null,"Disciplina",null,"512.55"]
[null,null,"Soggetti",null,"Algebraic geometry"]
[{"$nulls":4},"Matrix theory"]
[{"$nulls":4},"Algebra"]
[{"$nulls":4},"Algebraic Geometry"]
[{"$nulls":4},"Linear and Multilinear Algebras, Matrix Theory"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,"Nota di contenuto",null,"1 Introduction -- 2 Nonabelian Jacobian J(X; L; d): main properties -- 3 Some properties of the filtration H -- 4 The sheaf of Lie algebras G -- 5 Period maps and Torelli problems -- 6 sl2-structures on F -- 7 sl2-structures on G -- 8 Involution on G -- 9 Stratification of T -- 10 Configurations and theirs equations -- 11 Representation theoretic constructions -- 12 J(X; L; d) and the Langlands Duality."]
[null,null,null,"Sommario/riassunto","The Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and beautiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for smooth projective surfaces - a theory of the nonabelian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabelian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbert scheme of points. But it also comes equipped with the variation of Hodge-like structures, which produces a sheaf of reductive Lie algebras naturally attached to our Jacobian. This constitutes a nonabelian analogue of the (abelian) Lie algebra structure of the classical Jacobian. This feature naturally relates geometry of surfaces with the representation theory of reductive Lie algebras/groups. This work’s main focus is on providing an in-depth study of various aspects of this relation. It presents a substantial body of evidence that the sheaf of Lie algebras on the nonabelian Jacobian is an efficient tool for using "]
[{"$nulls":4},"the representation theory to systematically address various algebro-geometric problems. It also shows how to construct new invariants of representation theoretic origin on smooth projective surfaces."]