000 03451nam a22004695i 4500
001 978-3-642-35662-9
003 DE-He213
005 20190213151540.0
007 cr nn 008mamaa
008 130305s2013 gw | s |||| 0|eng d
020 _a9783642356629
_9978-3-642-35662-9
024 7 _a10.1007/978-3-642-35662-9
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aReider, Igor.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aNonabelian Jacobian of Projective Surfaces
_h[electronic resource] :
_bGeometry and Representation Theory /
_cby Igor Reider.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aVIII, 227 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2072
505 0 _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.
520 _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.
650 0 _aGeometry, algebraic.
650 0 _aMatrix theory.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M11094
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642356612
776 0 8 _iPrinted edition:
_z9783642356636
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2072
856 4 0 _uhttps://doi.org/10.1007/978-3-642-35662-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11056
_d11056