By Kunihiko Kodaira
Kodaira is a Fields Medal Prize Winner. (In the absence of a Nobel prize in arithmetic, they're considered as the top specialist honour a mathematician can attain.)
Kodaira is an honorary member of the London Mathematical Society.
Affordable softcover version of 1986 classic
Read or Download Complex Manifolds and Deformation of Complex Structures PDF
Similar algebraic geometry books
Now again in print, this very hot e-book has been up-to-date to mirror fresh advances within the thought of semistable coherent sheaves and their moduli areas, which come with moduli areas in optimistic attribute, moduli areas of central bundles and of complexes, Hilbert schemes of issues on surfaces, derived different types of coherent sheaves, and moduli areas of sheaves on Calabi-Yau threefolds.
This survey covers teams of homotopy self-equivalence periods of topological areas, and the homotopy form of areas of homotopy self-equivalences. For manifolds, the total staff of equivalences and the mapping type crew are in comparison, as are the corresponding areas. integrated are equipment of calculation, a variety of calculations, finite new release effects, Whitehead torsion and different components.
This publication lays the algebraic foundations of a Galois thought of linear distinction equations and indicates its dating to the analytic challenge of discovering meromorphic capabilities asymptotic to formal ideas of distinction equations. Classically, this latter query used to be attacked via Birkhoff and Tritzinsky and the current paintings corrects and tremendously generalizes their contributions.
- Analytic Theory of Abelian Varieties
- Torsors and rational points
- Brauer Groups in Ring Theory and Algebraic Geometry: Proceedings, Univ. of Antwerp Wilrijk, Belgium, Aug 17-28, 1981
- Algebraic Groups
- Moduli of Double EPW-Sextics
Extra info for Complex Manifolds and Deformation of Complex Structures
Since clearly G is fixed point free, W= W / G is a complex manifold and has a group structure as the quotient group of W by G. Thus W is a complex Lie group. S. A complex vector space C" is a complex Lie group with respect to the usual addition. Take 2n vectors Wj = (wj, ... , wj) E C" for j = 1, ... ,2n, such that these Wj are linearly independent over IR. Then Wj generate a discrete subgroup of C". Since a fundamental domain of G is compact, T" = C" / G is a compact commutative complex Lie group, which we call a complex torus.
I Corollary. Let f(z) be a holomorphic function in a domain of em, and S the analytic hypersurface defined by the equation f( z) = O. We assume 0 E S. Supppose fo( z) = 0 is a minimal equation of S at o. c (z) = 0 is a minimal equation of S at c for every c E S with Icl < E. 14. Let U be a domain where f( z) is defined. f( z) = 0 is called a minimal equation of S in U if i (z) = 0 is a minimal equation of S at every c E S (\ U. 17, if f(z) = 0 and g(z) = 0 are both minimal equations of S in U, u(z) = f(z)/g(z) is a non-vanishing holomorphic function in U.
We may assume that OUj is a polydisk with centre Cj = Zj(q). Put g(w) = jj(c] + w(z] - c]), ... , cj+ w(zj - cj)). Then for (z], ... , zj) E ~,g( w) is a holomorphic function of won Iwl < 1 + 8 if 8 is sufficiently small, and Ig( w)1 attains its maximum at w = o. Consequently, by the maximum principle, g(w) is a constant. Thus jj(p) is a constant on ~, and, by the analytic continuation, one sees that f( p) is a constant on all of M. I In this section we give several examples of compact complex manifolds.
Complex Manifolds and Deformation of Complex Structures by Kunihiko Kodaira