Read e-book online Algebraic geometry. A concise dictionary PDF

By Elena Rubei

ISBN-10: 3110316226

ISBN-13: 9783110316223

Algebraic geometry has a sophisticated, tough language. This e-book 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 rookies that comprehend a few, yet no longer all, uncomplicated evidence of algebraic geometry to stick to seminars and to learn papers. The dictionary shape makes it effortless and speedy to refer to.

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Example text

Let ???? : (???????? , ???????? ) → (????, ????) be a pointed covering projection. The maps ????∗ : ???????? (???????? , ???????? ) → ???????? (????, ????) are injective for every ???? and are isomorphisms for ???? ≥ 2. Cremona transformations | 37 Theorem. Let ???? be a path-connected, locally path-connected, semi-locally simply connected topological space. Let ???? ∈ ????. There is a bijection between the following sets: {pointed covering maps on (????, ????)}/ pointed covering homeomorphisms and {subgroups of ????1 (????, ????)}, where a pointed covering homeomorphism between two pointed covering projections on (????, ????), ???????? : (???????? , ???????? ) → (????, ????) and ???????????? : (???????????? , ???????????? ) → (????, ????), is a homeomorphism ???? : ???????? → ???????????? such that ????(???????? ) = ???????????? and ???????????? ∘ ???? = ???????? .

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???? , (. . , ???????? , . ), (. . , ???????? , . ) ????→ (. . , ???????? ???????? , . ). Furthermore, ???????? (????) is the ????-secant variety to ???? (see [104]). Dimension. ([12], [104], [107], [159], [164], [185], [228]).

And {????1???? , . . , ???????????? } are two frames on an open subset ???? of ???? for the vector bundle ???? and, if ∑ ???????? ???????? = ∑ ???????????? ???????????? , then ????1???? ( ... ) = ???? ( ???????????? ????1 .. ) . ???????? Then, if ???? and ???????? are the connection matrices of ∇ with respect the two frames and ???? and ???????? are the matrices of the curvatures, we have that ???? = ????−1 ???????? + ????−1 ???????? ????, ???? = ????−1 ???????? ???? . Proposition. Let ∇ be a connection on a vector bundle ???? on ???? and ???? be its curvature. Let ????, ???? ∈ ????????.

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Algebraic geometry. A concise dictionary by Elena Rubei


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