We present some applications of the Macaulay2 software package SpecialFanoFourfolds, a package for working with Hodge-special cubic fourfolds and Hodge-special Gushel-Mukai fourfolds. In particular, we show how to construct new examples of such fourfolds, some of which turn out to be rational. We also describe how to calculate K3 surfaces associated with cubic or Gushel-Mukai fourfolds, which relies on an explicit unirationality of some moduli spaces of K3 surfaces.

Explicit Computations with Cubic Fourfolds, Gushel-Mukai Fourfolds, and their Associated K3 Surfaces

Stagliano, G
2023-01-01

Abstract

We present some applications of the Macaulay2 software package SpecialFanoFourfolds, a package for working with Hodge-special cubic fourfolds and Hodge-special Gushel-Mukai fourfolds. In particular, we show how to construct new examples of such fourfolds, some of which turn out to be rational. We also describe how to calculate K3 surfaces associated with cubic or Gushel-Mukai fourfolds, which relies on an explicit unirationality of some moduli spaces of K3 surfaces.
2023
Cubic fourfold
Gushel-Mukai fourfold
associated K3 surface
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/558742
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