LEADER 03744nam 22006135 450 001 9910733710003321 005 20200702064449.0 010 $a3-642-35662-1 024 7 $a10.1007/978-3-642-35662-9 035 $a(CKB)3280000000020590 035 $a(SSID)ssj0000880045 035 $a(PQKBManifestationID)11467978 035 $a(PQKBTitleCode)TC0000880045 035 $a(PQKBWorkID)10873277 035 $a(PQKB)11496970 035 $a(DE-He213)978-3-642-35662-9 035 $a(MiAaPQ)EBC3107049 035 $a(PPN)169138763 035 $a(EXLCZ)993280000000020590 100 $a20130305d2013 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNonabelian Jacobian of Projective Surfaces $eGeometry and Representation Theory /$fby Igor Reider 205 $a1st ed. 2013. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013. 215 $a1 online resource (VIII, 227 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2072 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-35661-3 327 $a1 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. 330 $aThe Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and beautiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for smooth projective surfaces - a theory of the nonabelian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabelian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbert scheme of points. But it also comes equipped with the variation of Hodge-like structures, which produces a sheaf of reductive Lie algebras naturally attached to our Jacobian. This constitutes a nonabelian analogue of the (abelian) Lie algebra structure of the classical Jacobian. This feature naturally relates geometry of surfaces with the representation theory of reductive Lie algebras/groups. This work?s main focus is on providing an in-depth study of various aspects of this relation. It presents a substantial body of evidence that the sheaf of Lie algebras on the nonabelian Jacobian is an efficient tool for using the representation theory to systematically address various algebro-geometric problems. It also shows how to construct new invariants of representation theoretic origin on smooth projective surfaces. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2072 606 $aAlgebraic geometry 606 $aMatrix theory 606 $aAlgebra 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 615 0$aAlgebraic geometry. 615 0$aMatrix theory. 615 0$aAlgebra. 615 14$aAlgebraic Geometry. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 676 $a512.55 700 $aReider$b Igor$4aut$4http://id.loc.gov/vocabulary/relators/aut$0479690 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910733710003321 996 $aNonabelian Jacobian of projective surfaces$9258677 997 $aUNINA