By Elena Rubei

Algebraic geometry has a classy, tough language. This publication includes a definition, a number of references and the statements of the most theorems (without proofs) for each of the commonest phrases during this topic. a few phrases of comparable topics are integrated. It is helping novices that comprehend a few, yet no longer all, easy proof of algebraic geometry to stick to seminars and to learn papers. The dictionary shape makes it effortless and quickly to consult.

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Additional info for Algebraic Geometry: A Concise Dictionary

Sample text

1, . . , ????. Let ???? be the matrix such that ????????,???? = ????????,???? . We have that ????1 (????) is the image ???? of the Segre embedding (see “Segre embedding”) ℙ????−1 × ℙ????−1 → ℙ???? , (. . , ???????? , . ), (. . , ???????? , . ) ????→ (. . , ???????? ???????? , . ).

43], [151], [153], [154], [160], [161], [218], [221]). , varieties parametrizing geometric objects of a certain kind. It was created to parametrize the possible complex structures on a fixed differentiable manifold. We recall that if ???? : ???? → ???? is a holomorphic surjective map between complex manifolds such that the differential of ???? at every point has maximal rank and the fibres of ???? are compact complex manifolds, then the fibres are diffeomorphic by Ehresmann’s theorem (see [58] or [149, Theorem.

Let ???? be an algebraically closed field. (1) We say that an algebraic set ???? over ???? is Cohen–Macaulay if, for any ???? ∈ ????, the local ring O????,???? (the stalk in ???? of the sheaf of the regular functions on ????) is Cohen– Macaulay. 26 | Cohen–Macaulay, Gorenstein, (arithmetically -,-) One can prove that a Cohen–Macaulay algebraic set is equidimensional: for instance, the union of a line and a plane meeting in a point is not Cohen–Macaulay. , removing a subvariety of codimension ≥ 2 cannot disconnect it.