Nonabelian Jacobian of Projective Surfaces : Geometry and Representation Theory / / by Igor Reider

• Autore: Reider Igor
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013
• Edizione: 1st ed. 2013.
• Descrizione fisica: 1 online resource (VIII, 227 p.)
• Disciplina: 512.55
• Soggetto topico: Algebraic geometry; Matrix theory; Algebra; Algebraic Geometry; Linear and Multilinear Algebras, Matrix Theory
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: 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.
• 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 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.
• Titolo autorizzato: Nonabelian Jacobian of projective surfaces
• ISBN: 3-642-35662-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910733710003321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 2072