PLUCKER FORMULAS
Let f : X Pn be a map of a nonsingular projective curve X . It is given
by an invertible sheaf L of some degree d and a basis (s0 , . . . , sn ) of a linear
subspace V of H 0 (X, L). In coordinate-free way, we have a linear subspace
V H
Math. 412. Modern Algebra. Fall 2005/06
Instructor: Igor Dolgachev, 3064 EH, 763-0151
e-mail: [email protected], webpage: www.math.lsa.umich.edu/idolga/teaching.html
Textbook John R. Durbin , Modern Algebra: An Introduction. 5th edition, John Wiley and Son
Math. 632. Homework 3
1, 2. Hartshorne, Ex. 5.10, 5. 11.
3. Let A = R[T0 , . . . , Tn ] be the polynomial algebra graded by the condition deg(Ti ) = qi > 0
and X = ProjA. Show by an example, that OX (1) is not locally trivial in general and prove that
OX
Math. 632. Homework 2
1. Let k = F (t) be a purely transcendental extension of a eld F and K be an extension of k
obtained by adjoining a p-th root of t. Compute the Galois group scheme of the extension K/k .
2. Let F be a functor from the category of alg
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Introduction to Algebraic Geometry
Igor V. Dolgachev
April 30, 2010
ii
Contents
1 Systems of algebraic equations
1
2 Ane algebraic sets
7
3 Morphisms of ane algebraic varieties
13
4 Irreducible algebraic sets and rational functions
21
5 Projective algebra
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