The paper constructs infinite families of indecomposable motivic cycles on products of elliptic curves and conditionally links their regulators to algebraicity of higher Green's function values.
Motivic cycles on K3 double covers of del Pezzo surfaces
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abstract
We construct motivic cohomology cycles in the group $H^3_{\mathcal M}(Z,{\mathbb Q}(2))$ where $Z$ is a K3 surface obtained as a double cover of a del Pezzo surface $X$ branched at a curve in $|-2K_X|$. The construction uses (-1) curves on the del Pezzo and is a generalization of a recent pre-print of Ken Sato arXiv: 2408.09102 where he considers the case of fourfold covers of ${\mathbb P}^2$ branched at a quartic curve.
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Algebraic cycles and values of Green's functions -- Products of Elliptic Curves
The paper constructs infinite families of indecomposable motivic cycles on products of elliptic curves and conditionally links their regulators to algebraicity of higher Green's function values.