index.md

layout	page
title	FanoCats
fanos	0 1 5 18 124 866 7622
rhos	1 2 3 4 5 6 0 1 0 1 2 1 1 0 1 4 7 4 2 0 1 9 28 47 27 10 1 1 0 1 15 91 268 312 137 35 5 2 0 1 26 257 1318 2807 2204 771 186 39 11 1 1

{::options parse_block_html="true" /}

This website, inspired by Pieter Belmans' Fanography, is a tool for visually studying the derived categories of smooth fano toric varieties.

See [here]({{ site.baseurl }}/README) for an explainer. Please get in touch with me if you'd like to use the Macaulay2 package used for these computations.

Bug reports and contributions are welcome on GitHub.

Smooth Fano Toric Surfaces

{% include table.toric.html class='fano-2' varieties=site.data.fano-2 %}

Smooth Fano Toric Threefolds

{% include table.toric.html class='fano-3' varieties=site.data.fano-3 %}

Smooth Fano Toric 4,5,6-folds

The are respectively 124, 866, and 7622 smooth fano toric varieties in dimensions 4, 5, and 6, thus they are further broken up by Picard rank.

Note: this data is computed, but only available online in dim $\leq4$ or Picard rank $\leq3$, so gray links don't work yet.

<style> .pad7 { display: inline-block; width: 7ch; /* max length */ text-align: left; } </style> {% for dim in (2..6) %} {% assign max = page.rhos[dim] | size | minus: 1 %} {% endfor %}

$\dim$	$\operatorname{rk} \mathrm{Pic}$
${{ dim }}$ ({{ page.fanos[dim] }})	≤2 (1+{{ page.rhos[dim][2] }})     {% for rho in (3..max) %} 4 and rho > 3 %}style="color: gray"{% endif %}> {{ rho }} ({{ page.rhos[dim][rho] }})   {% endfor %}