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1. |
Record Nr. |
UNINA990002102040403321 |
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Autore |
Miller, Ronald E. |
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Titolo |
Input-output analysis : foundations and extensions / Ronald E. Miller, Peter D. Blair |
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Pubbl/distr/stampa |
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Englewood Cliffs : Prentice-Hall, 1985 |
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ISBN |
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Descrizione fisica |
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Disciplina |
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Locazione |
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Collocazione |
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VI A 834 |
F/3.01 MIL |
62 339 MIL |
XV I 200 |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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2. |
Record Nr. |
UNINA9910733710003321 |
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Autore |
Reider Igor |
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Titolo |
Nonabelian Jacobian of Projective Surfaces : Geometry and Representation Theory / / by Igor Reider |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013 |
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ISBN |
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Edizione |
[1st ed. 2013.] |
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Descrizione fisica |
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1 online resource (VIII, 227 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 2072 |
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Disciplina |
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Soggetti |
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Algebraic geometry |
Matrix theory |
Algebra |
Algebraic Geometry |
Linear and Multilinear Algebras, Matrix Theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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. |
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