000 | 03451nam a22004695i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/978-3-642-35662-9 _2doi |
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050 | 4 | _aQA564-609 | |
072 | 7 |
_aPBMW _2bicssc |
|
072 | 7 |
_aMAT012010 _2bisacsh |
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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. |
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300 |
_aVIII, 227 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2072 |
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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 |