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Positive del Pezzo geometry

  • Nick Early

    Institute for Advanced Study, Princeton, USA

  • Alheydis Geiger

    Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

  • Marta Panizzut

    UiT The Arctic University of Norway, Tromsø, Norway

  • Bernd Sturmfels

    Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

  • Claudia He Yun

    UiT The Arctic University of Norway, Tromsø, Norway
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Abstract

Real, complex, and tropical algebraic geometry join forces in a new branch of mathematical physics called positive geometry. We develop the positive geometry of del Pezzo surfaces and their moduli spaces, viewed as very affine varieties. Their connected components are derived from polyhedral spaces with Weyl group symmetries. We study their canonical forms and scattering amplitudes, and we solve the likelihood equations.

Cite this article

Nick Early, Alheydis Geiger, Marta Panizzut, Bernd Sturmfels, Claudia He Yun, Positive del Pezzo geometry. Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2025), published online first

DOI 10.4171/AIHPD/205