Jacobi-Bernoulli cohomology and deformations of schemes and maps

Ziv Ran

Open Mathematics (2012)

  • Volume: 10, Issue: 4, page 1541-1591
  • ISSN: 2391-5455

Abstract

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We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme X over ℂ, we construct a tangent SELA J X and show that the Jacobi-Bernoulli cohomology of J X is related to infinitesimal deformations of X.

How to cite

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Ziv Ran. "Jacobi-Bernoulli cohomology and deformations of schemes and maps." Open Mathematics 10.4 (2012): 1541-1591. <http://eudml.org/doc/269349>.

@article{ZivRan2012,
abstract = {We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme X over ℂ, we construct a tangent SELA J X and show that the Jacobi-Bernoulli cohomology of J X is related to infinitesimal deformations of X.},
author = {Ziv Ran},
journal = {Open Mathematics},
keywords = {Deformations; Schemes; Lie algebras; Bernoulli numbers; Cohomology; deformations; semi simplicial Lie algebra; SELA; Jacobi-Bernoulli complex; Baker-Campbell-Hausdorff formula; BCH polynomial; normal algebra; normal atom; tangent atom; Ischebeck's theorem},
language = {eng},
number = {4},
pages = {1541-1591},
title = {Jacobi-Bernoulli cohomology and deformations of schemes and maps},
url = {http://eudml.org/doc/269349},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Ziv Ran
TI - Jacobi-Bernoulli cohomology and deformations of schemes and maps
JO - Open Mathematics
PY - 2012
VL - 10
IS - 4
SP - 1541
EP - 1591
AB - We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme X over ℂ, we construct a tangent SELA J X and show that the Jacobi-Bernoulli cohomology of J X is related to infinitesimal deformations of X.
LA - eng
KW - Deformations; Schemes; Lie algebras; Bernoulli numbers; Cohomology; deformations; semi simplicial Lie algebra; SELA; Jacobi-Bernoulli complex; Baker-Campbell-Hausdorff formula; BCH polynomial; normal algebra; normal atom; tangent atom; Ischebeck's theorem
UR - http://eudml.org/doc/269349
ER -

References

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  10. [10] Ran Z., Enumerative geometry of families of singular plane curves, Invent. Math., 1989, 97(3), 447–465 http://dx.doi.org/10.1007/BF01388886 Zbl0702.14040
  11. [11] Ran Z., Stability of certain holomorphic maps, J. Differential Geom., 1991, 34(1), 37–47 Zbl0755.32017
  12. [12] Ran Z., Canonical infinitesimal deformations, J. Algebraic Geom., 2000, 9(1), 43–69 Zbl1060.14016
  13. [13] Ran Z., Lie atoms and their deformations, Geom. Funct. Anal., 2008, 18(1), 184–221 http://dx.doi.org/10.1007/s00039-008-0655-x Zbl1142.14007
  14. [14] Sernesi E., Deformations of Algebraic Schemes, Grundlehren Math. Wiss., 334, Springer, Berlin, 2006 Zbl1102.14001
  15. [15] Varadarajan V.S., Lie Groups, Lie Algebras and their Representations, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Englewood Cliffs, 1974 

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