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Projectively dual varieties. (English. Russian original) Zbl 1050.14048
J. Math. Sci., New York 117, No. 6, 4585-4732 (2003); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 100, 5-245 (2006).
Even 148 pages are not enough to review (with some proofs, several nice examples and 214 refences) all aspects related to the duality of projective varieties. The parts considered here are well-written and hence this survey is useful. Its strong points are: dual varieties of algebraic groups orbits; the Cayley method for discriminants (more extensively considered in the wonderful book of I. M. Gelfand, M. M. Kapranov and A. V. Zelevinski [“Discriminants, resultants, and multidimensional determinants” (1994; Zbl 0827.14036)]); resultants and schemes of zeroes. He considers also applications of Fulton-Hansen connectedness theorem and of Mori theory. The final chapter contains some less well-known applications. I found nice the one on relations discrimants and automorphisms and the one on quasiderivations of commutative algebras, but several readers will find here several different nice topics.

MSC:
14N05 Projective techniques in algebraic geometry
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