Algebraic Geometry Seminar: "Higher Chow cycles arising from some Laurent polynomials"

Abstract: An example of the constructions of Calabi-Yau hypersurface sections in a toric Fano variety is to consider a pencil defined by a Laurent polynomial.  We often can construct non-trivial families of higher Chow cycles from rational irreducible components on its base locus.
In this talk, we introduce two examples of such families of higher cycles and significant properties of the associated higher normal functions. The first one exhibits a B-model side explanation of Golyshev's Apéry constants on some rank one Fano threefolds defined via the quantum recursions. It is an example of the arithmetic mirror conjecture. The second one is defined on general cubic fourfolds containing a plane. Via the identification of the 2-torsion part of the Brauer group of the associated K3 surface and that of the indecomposable cycles, we expect that this family of higher cycles relates to the rationality problem.

Host: Matt Kerr