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Calabi-Yau operators of degree two

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arxiv 2103.08651 v1 pith:DKNT57FC submitted 2021-03-15 math.AG

classification math.AG
keywords operatorscalabi-yaudegreecomponentsfourthorderadmitarithmetically
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We show that the solutions to the equations defining the so-called Calabi-Yau condition for fourth order operators of degree two defines a variety that consists of ten irreducible components. These can be described completely in parametric form, but only two of the components seem to admit arithmetically interesting operators. We include a description of the 69 essentially distinct fourth order Calabi-Yau operators of degree two that are presently known to us.

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  1. Special Functions and Geometries in Scattering Amplitudes: From Particle Physics to Gravity

    hep-th 2025-06 conditional novelty 4.0 of 10

    The thesis performs the first elliptic symbol bootstrap to obtain the symbol of the two-loop twelve-point double box, and identifies the first Calabi-Yau threefold geometry in post-Minkowskian gravitational-wave integrals.

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