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We introduce the notion of multiplication kernels of birational and $D$-module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its quantization. Finally, we discuss geometric and algebraic aspects of method of separation of variables, and describe hypothetically a cyclic $D$-module for the generalized multiplication kernels for Hitchin systems for groups $GL_r$.
We compute equations for real multiplication on the divisor classes of genus two curves via algebraic correspondences. We do so by implementing van Wamelens method for computing equations for endomorphisms of Jacobians on examples drawn from the alge
A theorem by Orlov states that any equivalence between the bounded derived categories of coherent sheaves of two smooth projective varieties, X and Y, is isomorphic to a Fourier-Mukai transform with kernel in the bounded derived category of coherent
We prove that the generic point of a Hilbert modular four-fold is not a Jacobian. The proof uses degeneration techniques and is independent of properties of the mapping class group used in preceding papers on locally symmetric subvarieties of the mod
We construct a family of birational maps acting on two dimensional projective varieties, for which the growth of the degrees of the iterates is cubic. It is known that this growth can be bounded, linear, quadratic or exponential for such maps acting
The A64FX CPU powers the current number one supercomputer on the Top500 list. Although it is a traditional cache-based multicore processor, its peak performance and memory bandwidth rival accelerator devices. Generating efficient code for such a new