03744nam 22006135 450 991073371000332120200702064449.03-642-35662-110.1007/978-3-642-35662-9(CKB)3280000000020590(SSID)ssj0000880045(PQKBManifestationID)11467978(PQKBTitleCode)TC0000880045(PQKBWorkID)10873277(PQKB)11496970(DE-He213)978-3-642-35662-9(MiAaPQ)EBC3107049(PPN)169138763(EXLCZ)99328000000002059020130305d2013 u| 0engurnn|008mamaatxtccrNonabelian Jacobian of Projective Surfaces Geometry and Representation Theory /by Igor Reider1st ed. 2013.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2013.1 online resource (VIII, 227 p.) Lecture Notes in Mathematics,0075-8434 ;2072Bibliographic Level Mode of Issuance: Monograph3-642-35661-3 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.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.Lecture Notes in Mathematics,0075-8434 ;2072Algebraic geometryMatrix theoryAlgebraAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Algebraic geometry.Matrix theory.Algebra.Algebraic Geometry.Linear and Multilinear Algebras, Matrix Theory.512.55Reider Igorauthttp://id.loc.gov/vocabulary/relators/aut479690MiAaPQMiAaPQMiAaPQBOOK9910733710003321Nonabelian Jacobian of projective surfaces258677UNINA01009nam0 22002651i 450 UON0010278620231205102601.15520020107d1959 |0itac50 barusRU|||| 1||||Etruski v Severnoj ItaliiN. N. Zalesskij[Leningrad]Izdatel'stvo Leningradskoro Universiteta1959113 p.22 cmLingua etruscaStudiUONC025073FIRULeningradUONL003193499.94LINGUA ETRUSCA21ZALESSKIJN. N.UONV065888664764Izdatel'stvo Leningradskogo UniversitetaUONV251751650ITSOL20250613RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00102786SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI GLOTT B 7 III 020 SI MR 70536 5 020 Etruski v Severnoj Italii1311239UNIOR