ELI5 Hodge Conjecture > Let X be a non-singular complex…
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ELI5 Hodge Conjecture
> Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.
Every (non-degenerate) complex manifold within a projective space can be decomposed into a linear combination of subvarieties of X. The linear combination will somehow always use rational coefficients. (!!)
Is this conjecture assumed to be true by working mathematicians? Can you provide a little more information that would lend some intuition about Hodge, to an educated layperson?
#science
> Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.
Every (non-degenerate) complex manifold within a projective space can be decomposed into a linear combination of subvarieties of X. The linear combination will somehow always use rational coefficients. (!!)
Is this conjecture assumed to be true by working mathematicians? Can you provide a little more information that would lend some intuition about Hodge, to an educated layperson?
#science
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