4 papers · 1 filter
Known cases of the Hodge conjecture
Genival da Silva
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…
Notes on the Hodge Conjecture for Fermat Varieties
Genival da Silva
We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.
On the Topology of Fano Smoothings
Tom Coates, Alessio Corti, Genival da Silva
Suppose that X is a Fano manifold that corresponds under Mirror Symmetry to a Laurent polynomial f, and that P is the Newton polytope of f. In this setting it is expected that ther…
On the monodromy of elliptic surfaces
Genival da Silva
There have been several constructions of family of varieties with exceptional monodromy group. In most cases, these constructions give Hodge structures with high weight(Hodge numbe…