Quotient Criterion

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Varieties with nef anti-canonical: Surjective Albanese

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Regularity and Geometric Meaning

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

Tangent Spaces in Algebraic Geometry

Explores derivations and the Zariski tangent space in algebraic geometry, emphasizing their importance and practical applications.

Remarks about the Quotient

Explores the concept of the quotient in linearly reductive groups and varieties, discussing irreducibility, normality, and integral properties.

Adjunctions and Applications

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

Variety Defined as the Closure of VCA

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Modern Algebraic Geometry: Schemes and Affine Schemes

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.

Quotients: Geometrical Properties

Delves into the geometrical properties of quotients by linearly reductive groups, emphasizing the uniqueness of closed orbits and the concept of a geometric quotient.

The Coordinate Ring of a Linearly Reductive Group

Covers the properties of the coordinate ring of a linearly reductive group.

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.