Hodge Theory of Isolated Hypersurface Singularities

Hodge conjecture asserts that for particularly nice types of spaces called projective algebraic varieties the pieces called Hodge cycles are actually (rational linear) combinations of geometric pieces called algebraic cycles. Hodge theory concerns part of mathematics related to the above millennium prize problem initiated by William Hodge. It analysis the properties of objects known as Hodge structures. Hodge theory is closely related to other areas of science as physics field theories differential equations...