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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.
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