tailieunhanh - Deformation inequivalent complex conjugated complex structures and applications

We start from a short summary of our principal result from [KK]: An 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 generalize this result to higher dimensions and construct several series of higher dimensional compact complex manifolds having no homeomorphisms reversing the canonical class. | Turk J Math 26 (2002) , 1 – 25 ¨ ITAK ˙ c TUB Deformation inequivalent complex conjugated complex structures and applications Viatcheslav Kharlamov and Viktor Kulikov∗ Abstract We start from a short summary of our principal result from [KK]: an 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 generalize this result to higher dimensions and construct several series of higher dimensional compact complex manifolds having no homeomorphisms reversing the canonical class. After that, we resume and broaden the applications given in [KK] and [KK2], in particular, as a new application, we propose examples of (deformation) non equivalent symplectic structures with opposite canonical classes. 1. Introduction Many of achievements in real algebraic geometry appeared as applications of complex geometry. By contrary, the results of the present paper, which has grown from a solution of some questions from the real algebraic geometry, can be considered as applications in the opposite direction. They may be of an interest for symplectic geometry too. To state the principal questions we need to fix some definitions. We choose the language of complex analytic geometry since in this setting the results sometimes look stronger than if we restricted ourselves to algebraic or K¨ahler varieties, though the K¨ ahler hypothesis could simplify several proofs and could allow one to extend the set of examples. Thus, we define a real structure on a complex manifold X as an antiholomorphic involution c : X → X. By a deformation equivalence we mean the equivalence generated by local deformations of complex manifolds. Since we are interested only in compact manifolds, this, commonly used, local deformation equivalence relation can be defined in the following way: given a proper holomorphic submersion f : W → B1 , B1 = {|z| 2 there exists a compact complex .

• Toán học
• Complex algebraic surface
• Higher dimensions
• Non equivalent symplectic structures
• Opposite canonical classes
• Algebraic geometry
• Ebook Algebraic geometry 1
• Algebraic geometry 1
• Spectrum of a Ring
• Fiber products
• Schemes over fields
• Local Properties of Schemes
• Representable Functors
• Arithmetic curves
• Commutative algebra
• General properties of schemes
• Morphisms and base change
• Algebraic Geometry I
• Ebook Robin Hartshorne Algebraic
• Robin Hartshorne
• Projective Varieties
• Rationnal maps
• Nonsingular arieties
• Topics In Algebra Elementary Algebraic Geometry
• giáo trình toán học
• toán cao cấp
• bài giảng toán học
• Birational isomorphism
• Birational map
• Birational transformation
• Cremona group
• Classic algebraic geometry
• Paradigm shift 1 sheaves
• Paradigm shift 2 functors
• Natural transformations
• Other properties of functors
• Algorithms for Polynomials
• Algebraic Sets
• Algebraic Varieties
• Complete Varieties
• Dimension Theory
• period relative
• pessimistic beliefs
• Future Potentials
• Natural Fiber Polymer
• Composites Technology Applied
• Recovery and Protection
• height pairing
• introduction
• heigher function
• heigher dimensional
• hyperbolic analysis
• homomorphisms
• Modules
• Artinian rings
• Jacobson rings
• Zariski’s main theorem
• Morphisms of affine schemes
• institutional ownership
• provides evidence
• Thermoplastic Matrix
• Towpregs
• Wood Plastic
• Curing Monitoring
• Bài viết nghiên cứu khoa học
• Cohen Macaulayness
• Rees algebras
• Equimultiple ideals
• Algebraic Geometry and Commutative Algebra