Principles of Algebraic Geometry

1994/08/02 by Phillip Griffiths, Joseph Harris · 32 citations
Computer Science · Engineering · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic geometry #Algebraic geometry and analytic geometry #Algebraic number #Algebraic surface #Computer science #Engineering #Function field of an algebraic variety #Intuition #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Mathematics and Applications #Polynomial and algebraic computation #Pure mathematics #Quadric #Real algebraic geometry

paper · doi:10.1002/9781118032527

openalex publication_date 1994/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

Abstract

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top

Cited by

• The Tate Conjecture for a family of surfaces of general type with p g = q = 1 and K 2 = 3
• Harmonic Cheeger–Simons characters with applications
• The Geometry of Schemes
• Unraveling \mathcal L_{n, k} : grassmannian kinematics
• Threefolds in ℙ5with One Apparent Quadruple Point
• Integrable symplectic maps associated with discrete Korteweg-de Vries-type equations
• Classification and nondegeneracy of SU(n+1) Toda system with singular sources
• Vortices and Jacobian varieties
• The limiting behavior of the Liu-Yau quasi-local energy
• Fano Varieties in Mori Fibre Spaces
• Lectures on Kähler Geometry
• Stringy cosmic strings and noncompact Calabi-Yau manifolds
• Continuous and Smooth Envelopes of Topological Algebras. Part 2
• Toric reduction and a conjecture of Batyrev and Materov
• Differentiable Manifolds
• Tschirnhaus-Weierstrass curves
• Instanton moduli in string theory
• Correlators with sℓ 2 Yangian symmetry
• Complex Algebraic Surfaces
• Topological properties of quantum periodic Hamiltonians
• Complete Endomorphisms in Computer Vision
• Numerical Hermitian Yang-Mills connections and Kähler cone substructure
• Cohomology of compact hyperkaehler manifolds
• String theory beyond the Planck scale
• Non-Birational Twisted Derived Equivalences in Abelian GLSMs
• Cohomology theories on locally conformal symplectic manifolds
• Polynomial invariants for smooth four-manifolds
• Generic Initial Ideals
• Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry
• Irrationality and the h-cobordism conjecture
• Euler characteristics of Teichmüller curves in genus two
• Mirror symmetry, Langlands duality, and the Hitchin system
• Existence, decomposition, and limits of certain Weierstrass points
• Intermediate Jacobian [wikipedia]
• Nakayama's lemma [wikipedia]
• Riemann–Roch theorem [wikipedia]
• Sheaf cohomology [wikipedia]
• Tautological bundle [wikipedia]