introduction to algebraic geometry - dolgachev

Ngày tải lên: 31/03/2014, 15:08

... . So there is a one -to- one correspondence between radical ideals and algebraic sets. Corollary 2. If I is a prime ideal, then V (I ) is irreducible. There is a one -to- one cor- respondence between ... A 3 (C) into irreducible compo- nents. (b) Let V = {(t, t 2 , t 3 ) ∈ A 3 (C) | t ∈ C}. Find I (V ), and show that V is irre- ducible. ALGEBRAIC CURVES An Introduction to Algebraic...

Ngày tải lên: 31/03/2014, 12:20

... ADVANCED STUDIES Trieste U. Bruzzo INTRODUCTION TO ALGEBRAIC TOPOLOGY AND ALGEBRAIC GEOMETRY Notes of a course delivered during the academic year 2002/2003 14 1. INTRODUCTORY MATERIAL 4.5. The van Kampen ... are homotopic. Definition 1.3. One says that two topological spaces X, Y are homotopically equi- valent if there are continuous maps f : X → Y , g : Y → X such that g ◦ f is hom...

Ngày tải lên: 31/03/2014, 16:26

... FORMS Let ω be a connected and simply-connected open subset of R 2 . Together, The- orems 2. 8-1 and 2. 9-1 establish the existence of a mapping F that associates to any pair of matrix fields (a αβ ) ... such an immersion exists, to what extent is it unique? As shown in Theorems 1. 6-1 and 1. 7-1 , the answers turn out to be remarkably simple to state (but not so simple to pr...

Ngày tải lên: 17/03/2014, 14:24

...         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … -2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3 … -2 x 2 x n …………… -2 x n x 1 -2 x n x 2 -2 x n x 3 …  r 2 -2 (x n ) 2           -x 2 x 1 0 0 … 0 ... 1 r 4         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … -2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3 … -2...

Ngày tải lên: 27/03/2014, 11:52

...         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … !-2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3 … !-2 x 2 x n … … … … … -2 x n x 1 !-2 x n x 2 !-2 x n x 3 … ! r 2 -2 (x n ) 2         -x 2 x 1 0 0 … 0 ... 1 r 4         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … !-2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3...

Ngày tải lên: 24/04/2014, 17:08

... x’ -+ x + x’ and x @ x’ -+ x - x’ (ii) This homomorphism factorizes through the isomorphism M/c ~-~ (F) N (M/N)/F. This description of cl-’(F) needs no comment. The factorization ... E) is a system of generators of M. Definition 2.7 Let M and N be A - modules. A map f : M -+ N is a homo - morphism of A - modules (or is A -...

Ngày tải lên: 22/03/2014, 15:21

... (though they may be more convenient to work with). To see why, note that we can write a complex n-by-n matrix A + Bi (where A and B are real n-by-n matrices) as the 2n-by-2n matrix  A −B BA  .Inthisway,wecanembedGL(n, ... homomorphism ρ: G → GL(V )forsomevector space V called the representation space. Such a representa- tion is said to be faithful (resp., almost faithful )ifρ is one -...

Ngày tải lên: 31/03/2014, 16:15

Ngày tải lên: 24/04/2014, 17:09