Introduction to Algebraic Curves
American Mathematical Soc. - 225 pages
This book is an ideal introductory text as it provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. It includes numerous exercises.
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The Normalization Theorem and its Applications
The RiemannRoch Theorem
Applications of the RiemannRoch Theorem
Abels Theorem and 1ts Applications
1n fact 1n order Abel-Jacobi map affine equation algebraic geometry algebraic variety Bezout's theorem biholomorphic called canonical curve canonical map Chapter choose coefficients compact Riemann surface complex manifold complex numbers complex projective consider coordinate system curve components curve of degree curve of genus defined Definition degD denote differential one-form discussion Div(C divisor Exercise exists Figure finite number flex genus formula genus g Hence holomorphic coordinate holomorphic differential holomorphic function holomorphic mapping homogeneous polynomial hyperplane hypersurface injective intersection irreducible algebraic curve Lemma linearly independent meromorphic differential meromorphic function multiplicity neighborhood nontrivial normalization open set ordinary double points period matrix plane algebraic curve pole projective space proof of Proposition Proposition 1.7 prove Riemann sphere Riemann-Roch theorem satisfies singular points smooth point straight line subspace Suppose surface of genus tangent line theory topological variables Weierstrass polynomial yv(x zero