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Download Algebraic Geometry: A Concise Dictionary by Elena Rubei PDF

By Elena Rubei

ISBN-10: 3110316226

ISBN-13: 9783110316223

Algebraic geometry has a sophisticated, tricky 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 incorporated. It is helping rookies that be aware of a few, yet no longer all, uncomplicated evidence of algebraic geometry to persist with seminars and to learn papers. The dictionary shape makes it effortless and fast to consult.

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Extra resources for Algebraic Geometry: A Concise Dictionary

Example text

For some ???? and some ideal ????. In particular, if ???? is a smooth point of an algebraic variety ???? of dimension ???? over a field ????, then the completion of O????,???? is isomorphic to ????[[????1 , . . , ???????? ]]. See “Regular rings, smooth points, singular points”. Complexes. Let ???? be a ring. A complex of ????-modules, which is usually written ⋅⋅⋅ ????????−2 G ????????−1 ????????−1 G ???????? ???????? G ????????+1 ????????+1 G ⋅⋅⋅ , is the datum of a sequence of ????-modules ???????? and ????-homomorphisms ???????? : ???????? → ????????+1 such that ????????+1 ∘ ???????? = 0 for any ????.

There exist ???? neighborhood of ???????? in ???????? and ???? : ???? → ???? such that the deformation ???????? |???? (in the obvious sense) is isomorphic to the pull-back of ???? : ???? → (????, ????) through ????. We say that ???? : ???? → (????, ????) is universal if it is complete and the map ???? is locally unique. We say that ???? : ???? → (????, ????) is semiuniversal if it is complete and the map ???????????????? (the differential of ???? in ???????? ) is unique. 40 | Deformations Observe that all the universal deformations of a complex manifold ???? are locally canonically isomorphic, and all the semiuniversal deformations of ???? are locally isomorphic.

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: and {pointed covering maps on (????, ????)}/ pointed covering homeomorphisms {subgroups of ????1 (????, ????)}, where a pointed covering homeomorphism between two pointed covering projections on (????, ????), ???????? : (???????? , ???????? ) → (????, ????) and ???????????? : (???????????? , ???????????? ) → (????, ????), is a homeomorphism ???? : ???????? → ???????????? such that ????(???????? ) = ???????????? and ???????????? ∘ ???? = ???????? .

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Algebraic Geometry: A Concise Dictionary by Elena Rubei


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