Download E-books Several Complex Variables with Connections to Algebraic Geometry and Lie Groups (Graduate Studies in Mathematics, V. 46) PDF

By Joseph L. Taylor

This article offers an built-in improvement of the speculation of numerous complicated variables and intricate algebraic geometry, resulting in proofs of Serre's celebrated GAGA theorems referring to the 2 topics, and together with functions to the illustration idea of advanced semisimple Lie teams. It incorporates a thorough therapy of the neighborhood concept utilizing the instruments of commutative algebra, an in depth improvement of sheaf idea and the speculation of coherent analytic and algebraic sheaves, proofs of the most vanishing theorems for those different types of sheaves, and an entire evidence of the finite dimensionality of the cohomology of coherent sheaves on compact types. The vanishing theorems have a wide selection of functions and those are coated intimately. Of specific curiosity are the final 3 chapters, that are dedicated to purposes of the previous fabric to the examine of the constitution and representations of complicated semisimple Lie groups.Included during this textual content are introductions to harmonic research, the Peter-Weyl theorem, Lie concept and the constitution of Lie algebras, semisimple Lie algebras and their representations, algebraic teams and the constitution of advanced semisimple Lie teams. All of this culminates in Milicic's evidence of the Borel-Weil-Bott theorem, which makes vast use of the cloth constructed past within the textual content. there are many examples and workouts in every one bankruptcy. this contemporary remedy of a vintage viewpoint will be an exceptional textual content for a graduate path on a number of complicated variables, in addition to an invaluable reference for the specialist.

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