Complete variety

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Projective Varieties: Invariants and Dimensions

Covers invariants and dimensions of projective varieties, emphasizing their importance.

Automorphisms of Projective Varieties

Explores automorphisms of projective varieties, discussing isomorphism between complements and key observations on dimensions and examples.

Albanese and Fourier Transform: Positive Characteristic

Explores Albanese varieties, Fourier-Mukai transforms, and positive characteristic applications.

Projective Varieties: An Algebraic Study

Covers the study of projective varieties and their relation to compact manifolds.

Tangent Spaces in Algebraic Geometry

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Dimension of Algebraic Variety

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Complex Manifolds: GAGA Principle

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Riemann Zeta Function

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.

Algebraic Varieties in Linear Algebra

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.