# Principles of Algebraic Geometry

@inproceedings{Griffiths1978PrinciplesOA, title={Principles of Algebraic Geometry}, author={Phillip A. Griffiths and Joe W. Harris}, year={1978} }

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…

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## 7,477 Citations

### A Theory of Duality for Algebraic Curves

- Mathematics
- 2010

We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an…

### Mathematics and Statistics The geometry of second symmetric products of curves

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- 2009

This paper is a short summary of the main results in the thesis [1] and in the paper [40]. We deal throughout with several problems on the surfaces obtained as second symmetric products of smooth…

### An introduction to Hodge theory and applications to algebraic geometry

- Mathematics
- 2015

In this article, we develop the basic ideas behind the Hodge theorem on harmonic forms and the Hodge identities and decomposition for Kähler manifolds. We then use these ideas to obtain results such…

### Geometric Methods in Partial Differential Equations

- MathematicsMilan Journal of Mathematics
- 2021

We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of spaces associated to…

### Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31

- Mathematics
- 1984

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular…

### The geometry of second symmetric product of curves

- Mathematics
- 2009

This paper is a short summary of the main results in the thesis [1] and in the paper [40]. We deal throughout with several problems on the surfaces obtained as second symmetric products of smooth…

### on curves, surfaces and projective varieties. A classical view of algebraic geometry.

- Mathematics
- 2022

Under this respect, after reading the book, the student will ﬁnd that some gap must be ﬁlled, before he can handle the modern terminology. So, the book remains at a level which is more elementary…

### Algebraic Surfaces in Positive Characteristic

- Physics
- 2013

These notes grew out of a series of lectures given at Sogang University, Seoul, in October 2009. They were meant for complex geometers, who are not familiar with characteristic-p-geometry but who…

### Algebraic Geometry: An Introduction

- Mathematics
- 2007

Affine algebraic sets.- Projective algebraic sets.- Sheaves and varieties.- Dimension.- Tangent spaces and singular points.- Bezout's theorem.- Sheaf cohomology.- Arithmetic genus of curves and the…

### Rational varieties: algebra, geometry and arithmetic

- Mathematics
- 1986

CONTENTS Introduction § 1. Curves: geometry and arithmetic § 2. Surfaces: geometry over a closed field § 3. Surfaces: geometry over a non-closed field § 4. k-birational invariants § 5. Torsors and…