Jacobi-Bernoulli cohomology and deformations of schemes and maps

• Autorzy: Ziv Ran
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Deformations; Schemes; Lie algebras; Bernoulli numbers; Cohomology

Kategorie tematyczne

• 58H15: Deformations of structures
• 14D15: Formal methods; deformations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 4
• Strony: 1541-1591

Daty

wydano

2012-08-01

online

2012-05-31

Twórcy

autor

Ziv Ran

• University of California, Surge Facility

Bibliografia

• [1] Harris J., Mumford D., On the Kodaira dimension of the moduli space of curves, Invent. Math., 1982, 67(1), 23–88 http://dx.doi.org/10.1007/BF01393371
• [2] Hartshorne R., Algebraic Geometry, Grad. Texts in Math., 52, Springer, Berlin-New York-Heidelberg, 1977
• [3] Ischebeck F., Eine Dualität zwischen den Funktoren Ext und Tor, J. Algebra, 1969, 11(4), 510–531 http://dx.doi.org/10.1016/0021-8693(69)90090-8
• [4] Kodaira K., A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds, Ann. of Math., 1962, 75(1), 146–162 http://dx.doi.org/10.2307/1970424
• [5] Kodaira K., Complex Manifolds and Deformations of Complex Structures, Grundlehren Math. Wiss., 283, Springer, Berlin-New York, 1986 http://dx.doi.org/10.1007/978-1-4613-8590-5
• [6] Lichtenbaum S., Schlessinger M., The cotangent complex of a morphism, Trans. Amer. Math. Soc., 1967, 128, 41–70 http://dx.doi.org/10.1090/S0002-9947-1967-0209339-1
• [7] Matsumura H., Commutative Algebra, 2nd ed., Math. Lecture Note Ser., 56, Benjamin/Cummings, Reading, 1980
• [8] Merkulov S.A., Operad of formal homogeneous spaces and Bernoulli numbers, Algebra Number Theory, 2008, 2(4), 407–433 http://dx.doi.org/10.2140/ant.2008.2.407
• [9] Petracci E., Universal representations of Lie algebras by coderivations, Bull. Sci. Math., 2003, 127(5), 439–465 http://dx.doi.org/10.1016/S0007-4497(03)00041-1
• [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
• [11] Ran Z., Stability of certain holomorphic maps, J. Differential Geom., 1991, 34(1), 37–47
• [12] Ran Z., Canonical infinitesimal deformations, J. Algebraic Geom., 2000, 9(1), 43–69
• [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
• [14] Sernesi E., Deformations of Algebraic Schemes, Grundlehren Math. Wiss., 334, Springer, Berlin, 2006
• [15] Varadarajan V.S., Lie Groups, Lie Algebras and their Representations, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Englewood Cliffs, 1974

Identyfikatory

DOI

10.2478/s11533-012-0006-x