Known cases of the Hodge conjecture
Genival da Silva Jr
TL;DR
This survey reviews the known cases where the Hodge conjecture has been proven and discusses an approach by Griffiths-Green to potentially resolve the problem.
Contribution
It provides a comprehensive overview of established results and explores a promising approach by Griffiths-Green for solving the Hodge conjecture.
Findings
Summary of known cases where the Hodge conjecture holds
Explanation of the Griffiths-Green approach
Discussion of open problems and future directions
Abstract
The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by Griffiths-Green to solve the problem.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications