Fano fourfolds of type A beta

zero loci on products of type A Grassmannians and flag varieties

About

A catalogue of Fano fourfolds presented as zero loci of homogeneous bundles on products of type A flag varieties.

This catalogue is a work in progress. See the Fanobase blog for more information.

Please contact us at [email protected] (or email one of us) if you have any comments, remarks, or questions.

Citing this database

BibLaTeX

@online{fanobase-type-a,
  name = {Fano fourfolds in type A},
  title = {Fano fourfolds in type {A}},
  url = {https://type-a.fanobase.net/}
}

BibTeX

@other{fanobase-type-a,
  name = {Fano fourfolds in type A},
  title = {Fano fourfolds in type {A}},
  howpublished = {\url{https://type-a.fanobase.net/}}
}

Provenance of the data

The sheaf cohomology computations use HomogeneousTools, in particular PartialFlagVarieties.jl. Quantum data are computed using gwflags. The geometric and birational descriptions are worked out by hand with assistance of AI.

Acknowledgements

Personal support

Javier Fernández Píriz was supported by the Luxembourg National Research Fund (FNR), through PRIDE23/18686085/GRACE.
Pieter Belmans was supported by the Dutch Research Council (NWO), through the Vidi project CatsINCAGe, and by the Netherlands eScience Center and Open Science NL through a Research Software Sustainability Fellowship (project 341).

Organizational support

French National Research Agency (ANR): FanoHK (ANR-20-CE40-0023).
The computations presented in this catalogue were carried out using the HPC facilities of the University of Luxembourg (UL-HPC).