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A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps

Published online by Cambridge University Press:  20 November 2018

Donatella Iacono
Donatella Iacono*
Affiliation:
Dipartimento di Matematica “G. Castelnuovo”, Sapienza Università di Roma, Italy e-mail: iacono@dm.uniba.it
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Abstract

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We study infinitesimal deformations of holomorphic maps of compact, complex, Kähler manifolds. In particular, we describe a generalization of Bloch's semiregularity map that annihilates obstructions to deform holomorphic maps with fixed codomain.

Keywords

13D1014D1514B10semiregularity mapobstruction theoryfunctors of Artin ringsdifferential graded Lie algebras

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011 , pp. 472 - 486
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Artin, M., Lectures on deformations of singularities. Tata Institute of Fundamental Research, Bombay, 1976.Google Scholar
[2] Behrend, K. and Fantechi, B., The intrinsic normal cone. Invent. Math. 128(1997), no. 1, 45–88. doi:10.1007/s002220050136Google Scholar
[3] Bloch, S., Semi-regularity and deRham cohomology. Invent. Math. 17(1972), 51–66. doi:10.1007/BF01390023Google Scholar
[4] Buchweitz, R.-O. and Flenner, H., A semiregularity map for modules and applications to deformations. Compos. Math. 137(2003), no. 2, 135–210. doi:10.1023/A:1023999012081Google Scholar
[5] Buchweitz, R.-O. and Milson, J. J., CR-geometry and deformations of isolated singularities. Mem. Amer. Math. Soc. 125(1997), no. 597.Google Scholar
[6] Clemens, H., Geometry of formal Kuranishi theory. Adv. Math. 198(2005), no. 1, 311–365. doi:10.1016/j.aim.2005.04.015Google Scholar
[7] Deligne, P., Griffiths, P., Morgan, J., and Sullivan, D., Real homotopy theory of Kähler manifolds. Invent. Math. 29(1975), no. 3, 245–274. doi:10.1007/BF01389853Google Scholar
[8] Fantechi, B. and Manetti, M., Obstruction calculus for functors of Artin rings. I. J. Algebra, 202(1998), no. 2, 541–576. doi:10.1006/jabr.1997.7239Google Scholar
[9] Fantechi, B. and Manetti, M., On the T 1 -lifting theorem. J. Algebraic Geom. 8(1999), no. 1, 31–39.Google Scholar
[10] Fiorenza, D., Manetti, M., L ∞ algebras, Cartan homotopies and period maps. arXiv:math.AG/0605297v1.Google Scholar
[11] Horikawa, E., On deformations of holomorphic maps I & II. J. Math. Soc. Japan 25(1973), 372–396; 26(1974), 647–667. doi:10.2969/jmsj/02530372Google Scholar
[12] Iacono, D., Differential Graded Lie Algebras and Deformations of Holomorphic Maps, Ph. D. Thesis, Roma, 2006, arXiv:math.AG/0701091Google Scholar
[13] Iacono, D., L ∞ -algebras and deformations of holomorphic maps. Int. Math. Res. Not. 8(2008), Art. ID rnn013, 36 pp.Google Scholar
[14] Kawamata, Y., Unobstructed deformations. II. J. Algebraic Geom. 4(1995), no. 2, 277–279.Google Scholar
[15] Kontsevich, M., Deformation quantization of Poisson manifolds. Lett. Math. Phys. 66(2003), no. 3, 157–216. doi:10.1023/B:MATH.0000027508.00421.bfGoogle Scholar
[16] Manetti, M., Cohomological constraint to deformations of compact Kähler manifolds. Adv. Math. 186(2004), no. 1, 125–142. doi:10.1016/j.aim.2003.07.010Google Scholar
[17] Manetti, M., Lectures on deformations of complex manifolds. Rend. Mat. Appl. (7) 24(2004), no. 1, 1–183.Google Scholar
[18] Manetti, M., Lie description of higher obstructions to deforming submanifolds. Ann. Sc. Norm. Super. Pisa Cl. Sci. 6(2007), no. 4, 631–659.Google Scholar
[19] Ran, Z., Semiregularity, obstructions and deformations of Hodge classes. Ann. Scuola Norm. Pisa Cl. Sci. 28(1999), no. 4, 809–820.Google Scholar
[20] Ran, Z., Universal variations of Hodge structure and Calabi-Yau-Schottky relations. Invent. Math. 138(1999), 425–449. doi:10.1007/s002220050382Google Scholar