1st Edition

Plane Algebraic Curves

By C. Orzech Copyright 1981
    240 Pages
    by CRC Press

    This book introduces the contemporary notions of algebraic varieties, morphisms of varieties, and adeles to the classical subject of plane curves over algebraically closed fields. It is useful for advanced undergraduate and beginning graduate students in mathematics.

    Preface

    PREREQUISITES

    SOME FACTS ABOUT POLYNOMIALS

    AFFINE PLANE CURVES

    TANGENT SPACES

    THE LOCAL RING AT THE POINT

    PROJECTIVE PLANE CURVES

    RATIONAL MAPPINGS, BIRATIONAL CORRESPPONDENCES AND ISOMOPHISMS OF CURVES

    EXAMPLES OF RATIONAL CURVES

    THE CORRESPONDENCE BETWEEN VALUATIONS AND POINTS

    AN OVERVIEW AND SIDEWAYS GLANCE

    DIVISORS

    THE DIVISOR OF A FUNCTION HAS DEGREE 0

    RIEMANN’S THEOREM

    THE GENUS OF A NONSINGULAR PLANE CURVE

    CURVES OF GENUS 0 AND 1

    A CLASSIFICATION OF ISOMORPHISM CLASSES OF CURVES OF GENUS 1

    THE GENUS OF A SINGULAR CURVE

    INFLECTION POINTS ON PLANE CURVES

    BEZOUT’S THEOREM

    ADDITION ON A NONSINGULAR CUBIC

    DERIVATIONS, DIFFERENTIALS AND THE CANONICAL CLASS

    ADELES AND THE RIEMANN-ROCH THEROEM

    Bibliography

    Notation

    Index

    Biography

    C. Orzech