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11,731
Generalized complex geometry
, 2007
"... Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and s ..."
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Cited by 295 (7 self)
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Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define
in Complex Geometry
"... Abstract. In complex geometry, the use of n-convexity and the use of ampleness of the normal bundle of a d-codimensional submanifold are quite difficult for n>0andd>1. The aim of this paper is to explain how some constructions on the cycle space (the Chow variety in the quasiprojective setting ..."
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Abstract. In complex geometry, the use of n-convexity and the use of ampleness of the normal bundle of a d-codimensional submanifold are quite difficult for n>0andd>1. The aim of this paper is to explain how some constructions on the cycle space (the Chow variety in the quasiprojective
Generalised Complex Geometry
, 2008
"... Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of degrees of freedom are respectively described by a symplectic ..."
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Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of degrees of freedom are respectively described by a symplectic
Complex Analysis and Complex Geometry
, 2009
"... Complex analysis and complex geometry can be viewed as two aspects of the same subject. The two are inseparable, as most work in the area involves interplay between analysis and geometry. The fundamental objects of the theory are complex manifolds and, more generally, complex spaces, holomorphic fun ..."
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Complex analysis and complex geometry can be viewed as two aspects of the same subject. The two are inseparable, as most work in the area involves interplay between analysis and geometry. The fundamental objects of the theory are complex manifolds and, more generally, complex spaces, holomorphic
COMPLEX GEOMETRY AND Supergeometry
, 2005
"... Complex geometry and supergeometry are closely entertwined in superstring perturbation theory, since perturbative superstring amplitudes are formulated in terms of supergeometry, and yet should reduce to integrals of holomorphic forms on the moduli space of punctured Riemann surfaces. The presence o ..."
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Cited by 5 (0 self)
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Complex geometry and supergeometry are closely entertwined in superstring perturbation theory, since perturbative superstring amplitudes are formulated in terms of supergeometry, and yet should reduce to integrals of holomorphic forms on the moduli space of punctured Riemann surfaces. The presence
i urbulent Diffusion in Channels of Complex Geometry
, 2000
"... Turbulent diffusion in channels of complex geometry ..."
Hyperbolicity in complex geometry
- In The legacy of Niels Henrik Abel
, 2004
"... Summary. A complex manifold is said to be hyperbolic if there exists no nonconstant holomorphic map from the affine complex line to it. We discuss the techniques and methods for the hyperbolicity problems for submanifolds and their complements in abelian varieties and the complex projective space. ..."
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Cited by 7 (0 self)
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of general type. Introduction A complex manifold X is said to be hyperbolic if there exists no nonconstant holomorphic map C → X. The hyperbolicity problem in complex geometry studies the conditions for a given complex manifold X to be hyperbolic. Hyperbolicity problems have a long history and trace back
Integrable systems and complex geometry.
- Lobachevskii Journal of Mathematics,
, 2009
"... Abstract-In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax representation of the equations of motion. These sys ..."
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Cited by 2 (2 self)
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Abstract-In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax representation of the equations of motion
Lectures on Generalized Complex Geometry and Supersymmetry
, 2006
"... These are the lecture notes from the 26th Winter School ”Geometry and Physics”, Czech Republic, Srni, January 14- 21, 2006. These lectures are an introduction into the realm of generalized geometry based on the tangent plus the cotangent bundle. In particular we discuss the relation of this geometry ..."
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Cited by 25 (4 self)
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of this geometry to physics, namely to two-dimensional field theories. We explain in detail the relation between generalized complex geometry and supersymmetry. We briefly review the generalized Kähler and generalized Calabi-Yau manifolds and explain their appearance in physics.
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