Toric differential forms and periods of complete intersections

Abstract

Let $n$ be an even natural number. We compute the periods of any $\frac{n}{2}$-dimensional complete intersection algebraic cycle inside an $n$-dimensional non-degenerated intersection of a projective simplicial toric variety. Using this information we determine the cycle class of such algebraic cycles. As part of the proof we develop a toric generalization of a classical theorem of Macaulay about complete intersection Artin Gorenstein rings, and we generalize an algebraic cup formula for residue forms due to Carlson and Griffiths to the toric setting.

References in corpus (1)

• On fake linear cycles inside Fermat varieties

Cited by in corpus (1)

• The quadratic Euler characteristic of a smooth projective same-degree complete intersection