The Hodge conjecture is difficult since complicated submanifolds are incredibly rigid objects (because These are described by polynomials). In truth, it is very hard to construct complex submanifolds, and there are hardly any of these. Proving that submanifolds exist with no constructing them (a very practical type of indirect reasoning) https://sociallytraffic.com/story4248496/a-simple-key-for-bos138-unveiled