A database of quartic surfaces

This is a proof-of-concept database to demonstrate the possibility of computing numerically Picard lattices and many other invariants related to projective quartic surfaces. The database contains more than 180,000 quartics obtained with a random walk starting from Fermat quartic {w4+ x4+ y4+ z4=0}. Find interesting examples by clicking on the graphs. With the invariant displayed here, we can only distinguish 127 equivalence classes. We are currently looking for faster ways to compute periods and for methods to exhibit wider variety of behavior.

the paper
Pierre Lairez and Emre Sertöz, “A numerical transcendental method in algebraic geometry” (2018)
the sagemath package numperiods
It underlies all the computations presented here. (Proper packaging and documentation is in progress.)
proof status
The results presented here rely on high precision numerical computation and we are unable to exclude that something wrong was infered (not to talk about possible bugs). The columns B and err in the table below give some informations about the reliability. The computed Picard group provably contains all curves of degree at most B. The value err is a heuristic upper bound on the probability that the computed Picard group contains a wrong element.
Picard ranks
Number of monomials
Absolute value of the discriminant and Picard ranks
Dimension of the endomorphism ring
Parity of Picard rank
selected quartics out of | reset all
Below is a pick of 100 of them (at most).

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