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Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-Space, by T.E. Venkata Balaji

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Characterizing Affine Varieties; Defining Morphisms between Affine Or Quasi-Affine Varieties, by T.E. Venkata Balaji

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Proof of the Algebraic Nature of Analytic Branches of the Functional Inverse of an Analytic Function at a Critical Point, by T.E. Venkata Balaji

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The Field of Rational Functions Or Function Field of a Variety-The Local Ring at the Generic Point, by T.E. Venkata Balaji

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The J-Invariant of a Complex Torus (Or) of an Algebraic Elliptic Curve, by T.E. Venkata Balaji

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Any Variety is a Smooth Hypersurface on an Open Dense Subset, by T.E. Venkata Balaji

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Proof of the Implicit Function Theorem: Topological Preliminaries, by T.E. Venkata Balaji

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Maximal Atlases and Holomorphic Maps of Riemann Surfaces, by T.E. Venkata Balaji

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Proof of Schwarz Lemma and Uniqueness of Riemann Mappings, by T.E. Venkata Balaji

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Characterizing Normality at a Point by the Zooming Process and the Motivation for Zalcman’s Lemma, by T.E. Venkata Balaji

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Measuring Distances to Infinity, the Function Infinity and Normal Convergence of Holomorphic Functions in the Spherical Metric, by T.E. Venkata Balaji

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Differential Or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc., by T.E. Venkata Balaji

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The Idea of a Riemann Surface, by T.E. Venkata Balaji

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Torsion-Freeness of the Fundamental Group of a Riemann Surface, by T.E. Venkata Balaji

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Proof of the Implicit Function Theorem: The Integral Formula for & Analyticity of the Explicit Function, by T.E. Venkata Balaji

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A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism onto the Upper Half-Plane, by T.E. Venkata Balaji

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Differential Or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc, by T.E. Venkata Balaji

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Univalent Analytic Functions have never-Zero Derivatives and are Analytic Isomorphisms, by T.E. Venkata Balaji

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The Uniqueness Property of the Weierstrass Phe-Function Associated to a Lattice in the Plane, by T.E. Venkata Balaji

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The Ubiquity of Meromorphic Functions: The Nerves of the Geometric Network Bridging Algebra, Analysis and Topology, by T.E. Venkata Balaji

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Orbits of the Integral Unimodular Group in the Upper Half-Plane, by T.E. Venkata Balaji

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Proofs of the Great and Little Picard Theorems, by T.E. Venkata Balaji

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The Monodromy Action, by T.E. Venkata Balaji

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Why should we Study Affine Coordinate Rings of Functions on Affine Varieties ?, by T.E. Venkata Balaji

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Geometric Meaning of Isomorphism of Local Rings-Local Rings are almost Global, by T.E. Venkata Balaji

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The Ring of Functions on a Basic Open Set in the Zariski Topology, by T.E. Venkata Balaji

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Basic Algebraic Geometry : Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity, by T.E. Venkata Balaji

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The Importance of Local Rings-A Morphism is an Isomorphism if it is a Homeomorphism and Induces Isomorphisms at the Level of Local Rings, by T.E. Venkata Balaji

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A first Classification of Riemann Surfaces, by T.E. Venkata Balaji

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Introduction to the Arzela-Ascoli Theorem: Passing from Abstract Compactness to Verifiable Equicontinuity, by T.E. Venkata Balaji

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