000			02120nam a22003015i 4500
001			66510
005			20211110155853.0
010			_a978-3-642-35662-9 _dcompra
090			_a66510
100			_a20150401d2013 k||y0pory50 ba
101			_aeng
102			_aDE
200			_aNonabelian jacobian of projective surfaces _bDocumento electrónico _egeometry and representation theory _fIgor Reider
210			_aBerlin, Heidelberg _cSpringer Berlin Heidelberg _d2013
215			_aVIII, 227 p.
225			_aLecture Notes in Mathematics
300			_aColocação: Online
303			_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.
606			_93839 _aGeometria algébrica
606			_951604 _aTeoria das representações
680			_aQA564
700			_962824 _aReider _bIgor
801			_aPT _gRPC
856			_uhttp://dx.doi.org/10.1007/978-3-642-35662-9
942			_2lcc _cF _n0