// Workers AI · dad joke modeWhat did the Burniat surface say? I'm burned out.

In mathematics, a Burniat surface is one of the surfaces of general type introduced by Pol Burniat (1966).

Invariants

The geometric genus and irregularity are both equal to 0. The Chern number $c_{1}^{2}$ is either 2, 3, 4, 5, or 6.

References

• Barth, Wolf P.; Hulek, Klaus; Peters, Chris A.M.; Van de Ven, Antonius (2004), Compact Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., vol. 4, Springer-Verlag, Berlin, ISBN 978-3-540-00832-3, MR 2030225
• Burniat, Pol (1966), "Sur les surfaces de genre P₁₂>1", Annali di Matematica Pura ed Applicata, Series 4, 71 (1): 1–24, doi:10.1007/BF02413731, ISSN 0003-4622, MR 0206810