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On blow-ups and resolutions of Hermitian-symplectic and strongly Gauduchon metrics

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In this note, we study the blow-ups of Hermitian-symplectic manifolds and strongly Gauduchon manifolds along a point or compact complex submanifold. We show that any Hermitian-symplectic (resp. strongly Gauduchon) orbifold has a Hermitian-symplectic (resp. strongly Gauduchon) resolution.

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References

  1. Alessandrini L., Bassanelli G.: Modifications of compact balanced manifolds. C. R. Acad. Sci. Paris Sér. I 320, 1517–1522 (1995)

    MATH  MathSciNet  Google Scholar 

  2. Blanchard A.: Sur les variétés analytiques complexes. Ann. Sci. École Norn. Sup. 73, 157–202 (1956)

    MATH  MathSciNet  Google Scholar 

  3. Cavalcanti G.R., Fernández M., Muñoz V.: Symplectic resolutions, Lefschetz property and formality. Adv. Math. 218, 576–599 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Enrietti N., Fino A., Vezzoni L.: Tamed Symplectic forms and Strong Kahler with torsion metrics. J. Symplectic Geom. 10, 203–223 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fernández M., Muñoz V.: An 8-dimensional non-formal simply-connected symplectic manifold. Ann. of Math. 167, 1045–1054 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fino A., Tomassini A.: Blow-ups and resolutions of strong Kähler with torsion metrics. Adv. Math. 221, 914–935 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gauduchon P.: Le théorème de l’excentricité nulle. C. R. Acad. Sci. Paris, S. A 285, 387–390 (1977)

    MATH  MathSciNet  Google Scholar 

  8. P. Griffiths and J. Harris, Principles of Algebraic Geometry, John Wiley Sons, Inc., New York, 1994

  9. H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, I, II, Ann. of Math. 79 (1964), 109–203, 205–326.

  10. Hironaka H.: Flattening theorems in complex analytic geometry. Amer. J. Math. 97, 503–547 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  11. D. D. Joyce, Compact Manifolds with Special Holonomy, Oxford Math. Monogr., Oxford Univ. Press, 2000.

  12. K. Kodaira and D.C. Spencer, On deformations of complex analytic structures, III. Stability theorems for complex structures, Ann. of Math. 71 (1960), 43–76.

  13. Michelsohn M.: On the existence of special metrics in complex geometry. Acta Math. 143, 261–295 (1982)

    Article  MathSciNet  Google Scholar 

  14. Popovici D.: Stability of strongly Gauduchon manifolds under modifications. J. Geom. Anal. 23, 653–659 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  15. Popovici D.: Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics. Invent. Math. 194, 515–534 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Streets J., Tian G.: A parabolic flow of pluriclosed metrics. Int. Math. Res. Not. 2010, 3101–3133 (2010)

    MATH  MathSciNet  Google Scholar 

  17. Verbitsky M.: Rational curves and special metrics on twistor spaces. Geom. Topol. 18, 897–909 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  18. C. Voisin, Hodge Theory and Complex Algebraic Geometry I, Cambridge Stud. Adv. Math. 76 Cambridge University Press 2003.

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Yang, S. On blow-ups and resolutions of Hermitian-symplectic and strongly Gauduchon metrics. Arch. Math. 104, 441–450 (2015). https://doi.org/10.1007/s00013-015-0754-5

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