We study the blow-up of a locally conformally symplectic manifold at some point, and show that such blow-up also admits a locally conformally symplectic structure.
Nous étudions l'éclatement d'une variété localement conformément symplectique en un certain point, et montrons que le blow-up admet aussi une structure localement conformément symplectique.
Accepted:
Published online:
Youming Chen 1; Song Yang 1
@article{CRMATH_2016__354_4_411_0, author = {Youming Chen and Song Yang}, title = {On the blow-up of points on locally conformally symplectic manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {411--414}, publisher = {Elsevier}, volume = {354}, number = {4}, year = {2016}, doi = {10.1016/j.crma.2016.01.002}, language = {en}, }
Youming Chen; Song Yang. On the blow-up of points on locally conformally symplectic manifolds. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 411-414. doi : 10.1016/j.crma.2016.01.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.002/
[1] Moser stability for locally conformally symplectic structures, Proc. Amer. Math. Soc., Volume 137 (2009), pp. 2419-2424
[2] Contact pairs and locally conformal symplectic structures, Harmonic Maps and Differential Geometry, Contemp. Math., vol. 542, Amer. Math. Soc., Providence, RI, 2011, pp. 85-98
[3] Some properties of locally conformal symplectic structures, Comment. Math. Helv., Volume 77 (2002), pp. 383-398
[4] Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics, 2014 | arXiv
[5] Symplectic resolutions, Lefschetz property and formality, Adv. Math., Volume 218 (2008), pp. 576-599
[6] Locally Conformal Kähler Geometry, Progress in Mathematics, vol. 155, Birkhäuser Boston, Inc., Boston, MA, 1998
[7] An 8-dimensional non-formal simply-connected symplectic manifold, Ann. Math., Volume 167 (2008), pp. 1045-1054
[8] Reduction for locally conformal symplectic manifolds, J. Geom. Phys., Volume 37 (2001), pp. 262-271
[9] A kind of even-dimensional differential geometry and its application to exterior calculus, Amer. J. Math., Volume 65 (1943), pp. 433-438
[10] Blowing-up points on locally conformally balanced manifolds, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014), pp. 715-718
[11] Examples of symplectic simply connected manifolds with no Kähler structure, J. Differ. Geom., Volume 20 (1984), pp. 267-277
[12] A report on locally conformally Kähler manifolds, Harmonic Maps and Differential Geometry, Contemp. Math., vol. 542, Amer. Math. Soc., Providence, RI, 2011, pp. 135-149
[13] Some examples of locally conformal Kähler manifolds, Rend. Semin. Mat. (Torino), Volume 40 (1982), pp. 81-92
[14] On locally conformal almost Kähler manifolds, Isr. J. Math., Volume 24 (1976), pp. 338-351
[15] Locally conformal symplectic manifolds, Int. J. Math. Math. Sci., Volume 8 (1985), pp. 521-536
[16] Blowing-up points on locally conformally Kähler manifolds, Bull. Math. Soc. Sci. Math. Roum., Volume 52 (2009), pp. 387-390
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