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Moduli spaces in positive geometry

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arxiv 2405.17332 v2 pith:75K2RRSK submitted 2024-05-27 math.AG hep-thmath.CO

classification math.AGhep-thmath.CO
keywords geometryamplitudesmodulipositiveassociatedbinarycachazo-he-yuandevelop
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These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M_{0,n} of n distinct points on P^1 as a positive geometry and a binary geometry. We develop mathematical formalism to study Cachazo-He-Yuan's scattering equations and the associated scalar and Yang-Mills amplitudes. We discuss open superstring amplitudes and relations to tropical geometry.

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Cited by 2 Pith papers

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  1. Positive geometries and canonical forms via mixed Hodge theory

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    Canonical forms of positive geometries are constructed from Hodge theory and are unique exactly for 'genus zero pairs', with new formulas for polytopes and hyperplane arrangements.

  2. Points on Rational Normal Curves and the ABCT Variety

    math.AG 2024-12 conditional novelty 6.0 of 10

    The paper derives a recursive formula for the cohomology class of the ABCT variety V(3,n) inside the Grassmannian G(3,n), using a determinantal realization and Porteous' formula, and matches special coefficients to Eu...

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