Holomorphic vector bundle

Related lectures (30)

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Covers the application of Serre Duality in the general case, focusing on line bundles and core concepts.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores the construction of Riemann surfaces from equilateral triangles and the dynamics of finite-type maps.

Explores Laurent series in complex analysis, emphasizing singularities, residues, and the Cauchy theorem.

Explores holomorphic maps, ramification points, and the genus of a modular curve.

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

Explores the Cauchy Theorem and its applications in complex analysis.

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Explores the Residues Theorem and the classification of holomorphic functions.

Covers vector bundles, locally free sheaves, depth, Serre twisting sheaf, and graded modules in algebraic geometry.

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

Covers the application of Cauchy equations and integral decomposition, addressing questions related to holomorphic functions and Jacobian matrices.

Covers conformal blocks and their significance in complex structures and moduli spaces.

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