Algebraic Curves and Riemann Surfaces

1995/04/17 by Rick Miranda · 9 citations
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Advanced Mathematical Identities

paper · doi:10.1090/gsm/005

openalex publication_date 1995/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

Riemann surfaces: Basic definitions Functions and maps More examples of Riemann surfaces Integration on Riemann surfaces Divisors and meromorphic functions Algebraic curves and the Riemann-Roch theorem Applications of Riemann-Roch Abel's theorem Sheaves and Cech cohomology Algebraic sheaves Invertible sheaves, line bundles, and \check H¹ References Index of notation Index of terminology.

Cited by

• A series of coverings of the regular n-gon
• Symplectic homology of complements of smooth divisors
• Classification of sextic curves in the Fano 3-fold V₅ with rational Galois covers in \mathbb P³
• On the Geometry of the Moduli Space of Real Binary Octics
• Hyperelliptic surfaces are Loewner
• An optimal systolic inequality for CAT(0) metrics in genus two
• Function of several complex variables [wikipedia]
• Homotopy groups of spheres [wikipedia]
• Riemann–Roch theorem [wikipedia]