ZeroLocus62 is a compact,
canonical encoding for bundles, zero loci, and degeneracy loci of completely
reducible vector bundles on partial flag varieties. The label
40.G is a quintic threefold, and
603.111 is the
Fano 3-fold 1-10, the zero locus of
$(\bigwedge^2 \mathcal{U}^\vee)^{\oplus 3}$ on $\mathrm{Gr}(3,7)$.
The format
A label has the shape <ambient>.<bundle>. The part before the dot encodes a
product of partial flag varieties, one Dynkin type, rank, and set of marked
nodes per factor; the part after the dot encodes the highest weights of the
summands of the bundle. A third form with two - separators encodes degeneracy
loci. Everything is written in the Base62 alphabet, the 62 characters
0–9, A–Z, a–z, which is where the name comes
from: labels stay short, and they are safe in URLs and filenames without any
escaping.
The format is canonical: summands and ambient factors are put in a prescribed order before encoding, so two systems describing the same zero locus produce the same string. That is exactly what you want when storing them in a database or communicating them across systems.
Now in the General registry
The repository ships the specification (currently v3.1.2, for the v3.1
format) together with reference implementations in Python, Julia, JavaScript,
and Macaulay2. The Julia one is now in the General registry, so installing it
is simply
using Pkg
Pkg.add("ZeroLocus62")
instead of the Pkg.add(url=..., subdir="julia") incantation from the
previous
posts.
For the full specification, worked examples, and a live decoder, see the website.