A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps
Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 472-486

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2011-012-3
Mots-clés : 13D10, 14D15, 14B10, semiregularity map, obstruction theory, functors of Artin rings, differential graded Lie algebras
Iacono, Donatella. A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps. Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 472-486. doi: 10.4153/CMB-2011-012-3
@article{10_4153_CMB_2011_012_3,
     author = {Iacono, Donatella},
     title = {A {Semiregularity} {Map} {Annihilating} {Obstructions} to {Deforming} {Holomorphic} {Maps}},
     journal = {Canadian mathematical bulletin},
     pages = {472--486},
     year = {2011},
     volume = {54},
     number = {3},
     doi = {10.4153/CMB-2011-012-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-012-3/}
}
TY  - JOUR
AU  - Iacono, Donatella
TI  - A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps
JO  - Canadian mathematical bulletin
PY  - 2011
SP  - 472
EP  - 486
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-012-3/
DO  - 10.4153/CMB-2011-012-3
ID  - 10_4153_CMB_2011_012_3
ER  - 
%0 Journal Article
%A Iacono, Donatella
%T A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps
%J Canadian mathematical bulletin
%D 2011
%P 472-486
%V 54
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-012-3/
%R 10.4153/CMB-2011-012-3
%F 10_4153_CMB_2011_012_3

[1] [1] Artin, M., Lectures on deformations of singularities. Tata Institute of Fundamental Research, Bombay, 1976. Google Scholar

[2] [2] Behrend, K. and Fantechi, B., The intrinsic normal cone. Invent. Math. 128(1997), no. 1, 45–88. doi:10.1007/s002220050136 Google Scholar

[3] [3] Bloch, S., Semi-regularity and deRham cohomology. Invent. Math. 17(1972), 51–66. doi:10.1007/BF01390023 Google Scholar

[4] [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:1023999012081 Google Scholar

[5] [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] [6] Clemens, H., Geometry of formal Kuranishi theory. Adv. Math. 198(2005), no. 1, 311–365. doi:10.1016/j.aim.2005.04.015 Google Scholar

[7] [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/BF01389853 Google Scholar

[8] [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.1997.7239 Google Scholar

[9] [9] Fantechi, B. and Manetti, M., On the T 1 -lifting theorem. J. Algebraic Geom. 8(1999), no. 1, 31–39. Google Scholar

[10] [10] Fiorenza, D., Manetti, M., L algebras, Cartan homotopies and period maps. arXiv:math.AG/0605297v1. Google Scholar

[11] [11] Horikawa, E., On deformations of holomorphic maps I & II. J. Math. Soc. Japan 25(1973), 372–396; (1974), 647–667. doi:10.2969/jmsj/02530372 Google Scholar

[12] [12] Iacono, D., Differential Graded Lie Algebras and Deformations of Holomorphic Maps, Ph. D. Thesis, Roma, 2006, arXiv:math.AG/0701091 Google Scholar

[13] [13] Iacono, D., L -algebras and deformations of holomorphic maps. Int. Math. Res. Not. 8(2008), Art. ID rnn013, 36 pp. Google Scholar

[14] [14] Kawamata, Y., Unobstructed deformations. II. J. Algebraic Geom. 4(1995), no. 2, 277–279. Google Scholar

[15] [15] Kontsevich, M., Deformation quantization of Poisson manifolds. Lett. Math. Phys. 66(2003), no. 3, 157–216. doi:10.1023/B:MATH.0000027508.00421.bf Google Scholar

[16] [16] Manetti, M., Cohomological constraint to deformations of compact Kähler manifolds. Adv. Math. 186(2004), no. 1, 125–142. doi:10.1016/j.aim.2003.07.010 Google Scholar

[17] [17] Manetti, M., Lectures on deformations of complex manifolds. Rend. Mat. Appl. (7) 24(2004), no. 1, 1–183. Google Scholar

[18] [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] [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] [20] Ran, Z., Universal variations of Hodge structure and Calabi-Yau-Schottky relations. Invent. Math. 138(1999), 425–449. doi:10.1007/s002220050382 Google Scholar

Cité par Sources :