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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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Infinity as an Essential Singularity and Transcendental Entire Functions, by T.E. Venkata Balaji

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General Or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of Convergence, by T.E. Venkata Balaji

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Homotopy and the first Fundamental Group, by T.E. Venkata Balaji

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The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane Curve, by T.E. Venkata Balaji

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Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian Fundamental Groups, by T.E. Venkata Balaji

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Continuity of Meromorphic Functions at Poles and Topologies of Spaces of Functions, by T.E. Venkata Balaji

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Going Back and Forth between Subsets and Ideals, by T.E. Venkata Balaji

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Existence and Uniqueness of Analytic Continuations on Nearby Paths, by T.E. Venkata Balaji

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The Universal Covering as a Hausdorff Topological Space, by T.E. Venkata Balaji

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Characterizing Moebius Transformations with a Single Fixed Point, by T.E. Venkata Balaji

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Translating Homogeneous Localisation into Geometry and Back, by T.E. Venkata Balaji

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Riemann Surface Structures on Cylinders and Tori Via Covering Spaces, by T.E. Venkata Balaji

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Translating Projective Geometry into Graded Rings and Homogeneous Ideals, by T.E. Venkata Balaji

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The Formula for the Local Ring at a Point of a Projective Variety Or Playing with Localisations, Quotients, Homogenisation and Dehomogenisation !, by T.E. Venkata Balaji

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Proof of the other Direction of Marty’s Theorem-The Meromorphic Avatar of the Montel & Arzela-Ascoli Theorems-Normal Sequential Compactness Implies Normal Uniform Boundedness of Spherical Derivatives, by T.E. Venkata Balaji

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The Necessity of Elliptic Functions for the Classification of Complex Tori, by T.E. Venkata Balaji

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The Fundamental Functional Equations Satisfied by the Modular Form of Weight Two on the Upper Half-Plane, by T.E. Venkata Balaji

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The Riemann Surface for the Functional Inverse of an Analytic Mapping at a Critical Point, by T.E. Venkata Balaji

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Expanding the Category of Varieties to Include Projective and Quasi-Projective Varieties, by T.E. Venkata Balaji

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Well-Definedness of the Spherical Derivative of a Meromorphic Function at a Pole and Inversion-Invariance of the Spherical Derivative, by T.E. Venkata Balaji

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The Ring of Polynomial Functions on an Affine Variety, by T.E. Venkata Balaji

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A Riemann Surface Structure on a Cylinder, by T.E. Venkata Balaji

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Translating Morphisms into Affines as K-Algebra Maps and the Grand Hilbert Nullstellensatz, by T.E. Venkata Balaji

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Completion of the Proof of the Inverse Function Theorem: The Integral Inversion Formula for the Inverse Function, by T.E. Venkata Balaji

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Gluing (N+1) Copies of Affine N-Space to Produce Projective N-Space in Topology, Manifold Theory and Algebraic Geometry; The Key to the Definition of a Homogeneous Ideal, by T.E. Venkata Balaji

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When is a Function Analytic at Infinity ?, by T.E. Venkata Balaji

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