Hartshorne Chapter 1. 6 Answers to Exercises

Book Id: WPLBN0000676332
Format Type: PDF eBook:
File Size: 0.1 MB
Reproduction Date: 2005

Title:	Hartshorne Chapter 1. 6 Answers to Exercises
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Hartshorne Chapter 1. 6 Answers to Exercises. (n.d.). Hartshorne Chapter 1. 6 Answers to Exercises. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: A By Y is isomorphic to an open subset of some projective space and therefore to a proper open subset of P and therefore to some open subset of A b We can assume Y A then Y is isomorphic to the subset y x a x. Any element of A Y can be written uniquely in the form a x b c x bncn with ci some integer and ci positive if bi is not one of a an Hence A Y is a U F D with primes x bi for bi a an a Singular points must satisfy y x x y x and if k does not have characteristic this implies y x which contradicts x The polynomial y x x is irreducible because if it were reducible then its two factors would intersect somewhere possibly at infinity and this point of intersection would be singular We should really also check that the curve has no singular points at infinity As Y is nonsingular all points of Y are normal so Y is normal so A Y is integrally closed ...