Abstract:
This paper sets forth the basic elements of the theory of complex superspaces, coherent sheaves on them and deformations of these objects. The existence of versal deformations is proved for various objects of superanalytical geometry — superspaces, sheaves on them, subsuperspaces, SUSY-curves and so on. A construction is described of families of supermanifolds that contain all supermanifolds with a given underlying or associated split manifold.
Citation:
A. Yu. Vaintrob, “Deformations of complex superspaces and of the coherent sheaves on them”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 32, VINITI, Moscow, 1988, 125–211; J. Soviet Math., 51:1 (1990), 2140–2188
\Bibitem{Vai88}
\by A.~Yu.~Vaintrob
\paper Deformations of complex superspaces and of the coherent sheaves on them
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1988
\vol 32
\pages 125--211
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd104}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=957753}
\zmath{https://zbmath.org/?q=an:0736.58003}
\transl
\jour J. Soviet Math.
\yr 1990
\vol 51
\issue 1
\pages 2140--2188
\crossref{https://doi.org/10.1007/BF01098187}
Linking options:
https://www.mathnet.ru/eng/intd104
https://www.mathnet.ru/eng/intd/v32/p125
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E. G. VISHNYAKOVA, “RIGIDITY OF FLAG SUPERMANIFOLDS”, Transformation Groups, 27:3 (2022), 1149
Ugo Bruzzo, Daniel Hernández Ruipérez, “The supermoduli of SUSY curves with Ramond punctures”, RACSAM, 115:3 (2021)
Kowshik Bettadapura, “On the problem of splitting deformations of super Riemann surfaces”, Lett Math Phys, 109:2 (2019), 381
Kowshik Bettadapura, “Obstructed thickenings and supermanifolds”, Journal of Geometry and Physics, 139 (2019), 25
Sergio Luigi Cacciatori, Simone Noja, “Projective superspaces in practice”, Journal of Geometry and Physics, 130 (2018), 40
R. Heluani, J. Van Ekeren, “Characters of topological N= 2 vertex algebras are Jacobi forms on the moduli space of elliptic supercurves”, Advances in Mathematics, 302 (2016), 551
Anton M. Zeitlin, “Superopers on Supercurves”, Lett Math Phys, 105:2 (2015), 149
Rita Fioresi, Stephen Diwen Kwok, Springer INdAM Series, 7, Advances in Lie Superalgebras, 2014, 101
S. Bouarroudj, P. Ya. Grozman, D. A. Leites, I. M. Shchepochkina, “Minkowski superspaces and superstrings as almost real–complex supermanifolds”, Theoret. and Math. Phys., 173:3 (2012), 1687–1708
Jeffrey M. Rabin, Lecture Notes in Mathematics, 2027, Supersymmetry in Mathematics and Physics, 2011, 241
Gregorio Falqui, Cesare Reina, Alessandro Zampa, “A note on the super Krichever map”, Journal of Geometry and Physics, 37:1-2 (2001), 169
M. J. Bergvelt, J. M. Rabin, “Supercurves, their Jacobians, and super KP equations”, Duke Math. J., 98:1 (1999)
J.A. Domínguez Pérez, D. Hernández Ruipérez, C. Sancho de Salas, “Global structures for the moduli of (punctured) super riemann surfaces”, Journal of Geometry and Physics, 21:3 (1997), 199
Arkady Vaintrob, “Conformal Lie superalgebras and moduli spaces”, Journal of Geometry and Physics, 15:2 (1995), 109
V.A. Bunegina, A.L. Onishchik, “Two families of flag supermanifolds”, Differential Geometry and its Applications, 4:4 (1994), 329
U. Bruzzo, J.A. Domínguez Pérez, “Line bundles over families of (super) Riemann surfaces. II: The graded case”, Journal of Geometry and Physics, 10:3 (1993), 269
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