2001/11/11 by Viatcheslav Kharlamov, V. Kharlamov, Kharlamov, V. +3 · 1 citation
Mathematics · #14J28 #14P25 #57S25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14J28 #msc:14P25 #msc:57S25
paper · pdf · doi:10.48550/arxiv.math/0111126
23 pages, AmS-TeX, few minor misprints corrected
openalex publication_date 2001/11/11 · arxiv created 2002/01/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Here, we resume and broaden the results concerned which appeared in math.AG/0101098 and math.AG/0104021. We start from summing up our example of a complex algebraic surface which is not deformation equivalent to its complex conjugate and which, moreover, has no homeomorphisms reversing the canonical class. Then, we construct several series of higher dimensional compact complex manifolds having the same property. We end with discussing applications to the Dif=Def problems, to the existence of diffeomorphic plane cuspidal curves non equivalent under equisingular deformations and to the existence of (deformation) non equivalent symplectic structures with opposite canonical classes.