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**About this book :- **
**Lecture Notes Algebraic Geometry III/IV ** written by
** Matt Kerr **

This book contain consist the lecture notes to an idea of algebraic geometry.

**Book Detail :- **
** Title: ** Lecture Notes Algebraic Geometry III/IV
** Edition: **
** Author(s): ** Matt Kerr
** Publisher: **
** Series: **
** Year: **
** Pages: ** 331
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: **
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**Book Contents :- **
**Lecture Notes Algebraic Geometry III/IV ** written by
** Matt Kerr **
cover the following topics.
**Introduction and Motivation**

Two theorems on conics in the plane, Riemann surfaces and algebraic curves, The normalization theorem, Lines, conics, and duality
**General definitions and results**

Complex manifolds and algebraic varieties, More on projective algebraic varieties, Smooth varieties as complex manifolds, The connectedness of algebraic curves, Hilbert’s nullstellensatz, Local analytic factorization of polynomials, Proof of the normalization theorem, Intersections of curves, Meromorphic 1-forms on a Riemann surface, The genus formula, Some applications of Bézout
**Cubic curves**

The singular cubic, Putting a nonsingular cubic in standard form, Canonical normalization of the Weierstrass cubic, Group law on the nonsingular cubic, Abel’s theorem for elliptic curves, The Poncelet problem, Periods of families of elliptic curves, Counting Fp-rational points on elliptic curves
** Curves of higher genus **

The algebraicity of global analytic objects, The Riemann-Roch Theorem, Applications of Riemann-Roch, I: special Riemann surfaces, Applications of Riemann-Roch, II: general Riemann surfaces, Abel’s Theorem, part I, Abel’s Theorem, part II
**Appendix: **

Genera of singular curves

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