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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
?1
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