Projective Morphisms: Theory and Applications

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Adjunctions and Applications

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

Geometric Objects in Algebra

Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Coherent Sheaves: Locally Ringed Space

Covers the definition of coherent sheaves and their properties in the context of algebraic geometry.

Modern Algebraic Geometry

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

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.

Quasi-coherence in Algebraic Geometry

Covers the concept of quasi-coherence in algebraic geometry, discussing the lifting of functions, sections of sheaves, and push forwards of coherent sheaves.

Varieties with nef anti-canonical: Surjective Albanese

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

Locally Noetherian Schemes

Covers the concept of locally Noetherian schemes in algebraic geometry.

Regularity and Geometric Meaning

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

Applications of Serre Duality

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.