Abstract:
This paper is devoted to an exposition of the structure theory of supermanifolds and bundles on them, a description of Serre duality on supermanifolds, investigation of inverse sheaves, definition of characteristic classes and proof of the Grothendieck–Riemann–Roch theorem for supermanifolds.
Citation:
A. A. Voronov, Yu. I. Manin, I. B. Penkov, “Elements of supergeometry”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 32, VINITI, Moscow, 1988, 3–25; J. Soviet Math., 51:1 (1990), 2069–2083
\Bibitem{VorManPen88}
\by A.~A.~Voronov, Yu.~I.~Manin, I.~B.~Penkov
\paper Elements of supergeometry
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1988
\vol 32
\pages 3--25
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd101}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=957750}
\zmath{https://zbmath.org/?q=an:0736.58004}
\transl
\jour J. Soviet Math.
\yr 1990
\vol 51
\issue 1
\pages 2069--2083
\crossref{https://doi.org/10.1007/BF01098184}
Linking options:
https://www.mathnet.ru/eng/intd101
https://www.mathnet.ru/eng/intd/v32/p3
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Alexander Polishchuk, “A0|1-Torsors, Quotients by Free A0|1-Actions, and Embeddings into Π-Projective Spaces and Super-Grassmannians G(1|1, n|n)”, Commun. Math. Phys., 402:2 (2023), 2011
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Simone Noja, “On the geometry of forms on supermanifolds”, Differential Geometry and its Applications, 88 (2023), 101999
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M. Roshandelbana, S. Varsaie, “Analytic approach to a generalization of Chern classes in supergeometry”, Asian-European J. Math., 15:10 (2022)
Alexander Sherman, “Spherical supervarieties”, Annales de l'Institut Fourier, 71:4 (2022), 1449
Ekaterina Shemyakova, Theodore Voronov, “On super Plücker embedding and cluster algebras”, Sel. Math. New Ser., 28:2 (2022)
Sergio Luigi Cacciatori, Simone Noja, “Projective superspaces in practice”, Journal of Geometry and Physics, 130 (2018), 40
Tadashi Taniguchi, “Super Characteristic Classes and Riemann-Roch Type Formula”, APM, 05:06 (2015), 353
Stephen Kwok, “The geometry of Π-invertible sheaves”, Journal of Geometry and Physics, 86 (2014), 134
Caroline Gruson, Vera Serganova, “Bernstein–Gelfand–Gelfand reciprocity and indecomposable projective modules for classical algebraic supergroups”, Mosc. Math. J., 13:2 (2013), 281–313
Vera Serganova, Progress in Mathematics, 295, Highlights in Lie Algebraic Methods, 2012, 65
Mikhail Kapranov, Eric Vasserot, “Supersymmetry and the formal loop space”, Advances in Mathematics, 227:3 (2011), 1078
Stephen Kwok, Lecture Notes in Mathematics, 2027, Supersymmetry in Mathematics and Physics, 2011, 139
S. L. Lyakhovich, E. A. Mosman, A. A. Sharapov, “On Characteristic Classes of Q-manifolds”, Funct. Anal. Appl., 42:1 (2008), 75–77
V. G. Drinfeld, V. A. Iskovskikh, A. I. Kostrikin, A. N. Tyurin, I. R. Shafarevich, “Yurii Ivanovich Manin (on his 60th birthday)”, Russian Math. Surveys, 52:4 (1997), 863–873
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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