Relative topology of real algebraic varieties in their complexifications

We investigate, for a given smooth closed manifold M, the existence of an algebraic model X for M (i.e., a nonsingular real algebraic variety diffeomorphic to M) such that some nonsingular projective complexification i:X-->X-C of X admits a retraction r:X-C-->X. If such an X exists, we show that M must be formal in the sense of Sullivan's minimal models, and that all rational Massey products on M are trivial.


Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem
Dosi (Dosiev), A. A. (IOP Publishing, 2009-11-01)
We study the absolute basis problem in algebras of holomorphic functions in non-commuting variables generating a finite-dimensional nilpotent Lie algebra g. This is motivated by J. L. Taylor's programme of non-commutative holomorphic functional calculus in the Lie algebra framework.
Stability criterion for second order linear impulsive differential equations with periodic coefficients
Guseinov, G. Sh.; Zafer, Ağacık (Wiley, 2008-01-01)
In this paper we obtain instability and stability criteria for second order linear impulsive differential equations with periodic coefficients. Further, a Lyapunov type inequality is also established. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
On entire rational maps of real surfaces
Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01)
In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
A classification of equivariant principal bundles over nonsingular toric varieties
Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2016-12-01)
We classify holomorphic as well as algebraic torus equivariant principal G-bundles over a nonsingular toric variety X, where G is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.
Chirality of real non-singular cubic fourfolds and their pure deformation classification
Finashin, Sergey (Springer Science and Business Media LLC, 2020-02-22)
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface non-singular. Here, we perform a finer classification giving a full answer to the chirality problem: which of real non-singular cubic hypersurfaces can not be continuously deformed to their mirror reflection.
Citation Formats
Y. Ozan, “Relative topology of real algebraic varieties in their complexifications,” PACIFIC JOURNAL OF MATHEMATICS, pp. 291–302, 2004, Accessed: 00, 2020. [Online]. Available: