nLab super Riemann surface




Complex geometry

Manifolds and cobordisms



A super Riemann surface is the analog of a Riemann surface in supergeometry.


A Riemann surface with spin structure that is also a branched cover of P (1|1)\mathbb{C}P^{(1 \vert 1)} is canonically endowed with the structure of a super Riemann surface with Ramond punctures? (Donagi-Witten 15). This implies that adinkras encode certain very special super Riemann surfaces Doran & Iga & Landweber & Mendez-Diez 13.


The concept of super Riemann surfaces originates with the following articles:

  • Daniel Friedan, Notes On String Theory and 2-Dimensional Conformal Field Theory. 1986

  • M.A. Baranov, Albert Schwarz, On the Multiloop Contribution to the String Theory Int.J.Mod.Phys., A2:1773, 1987

  • Yuri Manin, Critical Dimensions of String Theories and the Dualizing Sheaf on the Moduli Space of (Super) Curves, Funct.Anal.Appl., 20:244-245,


  • Steve Giddings, P. Nelson, The Geometry of super Riemann surfaces, Commun. Math. Phys., 116, (1988), 607

See also

Further discussion of the moduli space of super Riemann surfaces includes the following:

See also:

Discussion of super Riemann surfaces induced by supermultiplets for NN-extended d=1d = 1 supersymmetry – via adinkra symbols, is due to

Further discussion of supergeometric Teichmüller space:

Last revised on June 2, 2021 at 06:04:45. See the history of this page for a list of all contributions to it.