2007/05/05 by Polishchuk, Alexander
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0705.0772
We study subrings in the Chow ring \CH^*(A)\Bbb Q of an abelian variety A, stable under the Fourier transform with respect to an arbitrary polarization. We prove that by taking Pontryagin products of classes of dimension ≤ 1 one gets such a subring. We also show how to construct finite-dimensional Fourier-stable subrings in \CH^*(A)\Bbb Q. Another result concerns the relation between the Pontryagin product and the usual product on the \CH^*(A)\Bbb Q. We prove that the operator of the usual product with a cycle is a differential operator with respect to the Pontryagin product and compute its order in terms of the Beauville's decomposition of \CH^*(A)\Bbb Q.