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UNINA9910463026503321 |
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Autore |
Geck Meinolf |
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Titolo |
An introduction to algebraic geometry and algebraic groups [[electronic resource] /] / Meinolf Geck |
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Pubbl/distr/stampa |
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Oxford ; ; New York, : Oxford University Press, 2003 |
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ISBN |
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1-299-13293-6 |
0-19-166372-7 |
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Descrizione fisica |
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1 online resource (320 p.) |
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Collana |
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Oxford Graduate Texts in Mathematics ; ; v.10 |
Oxford graduate texts in mathematics ; ; 10 |
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Disciplina |
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Soggetti |
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Geometry, Algebraic |
Linear algebraic groups |
Electronic books. |
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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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First published in paperback 2013. |
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Nota di bibliografia |
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Includes bibliographical references (p. [298]-303) and index. |
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Nota di contenuto |
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Cover; Contents; 1 Algebraic sets and algebraic groups; 1.1 The Zariski topology on affine space; 1.2 Groebner bases and the Hilbert polynomial; 1.3 Regular maps, direct products, and algebraic groups; 1.4 The tangent space and non-singular points; 1.5 The Lie algebra of a linear algebraic group; 1.6 Groups with a split BN-pair; 1.7 BN-pairs in symplectic and orthogonal groups; 1.8 Bibliographic remarks and exercises; 2 Affine varieties and finite morphisms; 2.1 Hilbert's nullstellensatz and abstract affine varieties; 2.2 Finite morphisms and Chevalley's theorem |
2.3 Birational equivalences and normal varieties2.4 Linearization and generation of algebraic groups; 2.5 Group actions on affine varieties; 2.6 The unipotent variety of the special linear groups; 2.7 Bibliographic remarks and exercises; 3 Algebraic representations and Borel subgroups; 3.1 Algebraic representations, solvable groups, and tori; 3.2 The main theorem of elimination theory; 3.3 Grassmannian varieties and flag varieties; 3.4 Parabolic subgroups and Borel subgroups; 3.5 On the structure of Borel subgroups; 3.6 Bibliographic remarks and exercises |
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