MINOR ORAL/Algebraic Geometry Seminar: "Explicit Hodge-D-Conjecture for Some Families of K3 Surfaces"

Abstract: For a smooth projective complex variety, we can generalize the classical Hodge conjecture to Beilinson’s Hodge-$\mathcal{D}$-conjecture by considering the higher cycle map from the higher Chow groups to the Deligne cohomology. Xi Chen and James D.Lewis proved this conjecture for general $K3$ surfaces by using rational curves on singular $K3$ surfaces. On a certain type of $K3$ surfaces which can degenerate to a general hyperplane arrangement, we directly construct an enough number of higher Chow cycles to show the conjecture in an explicit way.