scholarly journals On holomorphic maps and Generalized Complex Geometry

2011 ◽  
Vol 61 (8) ◽  
pp. 1502-1515 ◽  
Author(s):  
Liviu Ornea ◽  
Radu Pantilie
Keyword(s):  
Complex Geometry ◽  
Holomorphic Maps ◽  
Generalized Complex

scholarly journals Gaugino mass term for D-branes and Generalized Complex Geometry

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Mariana Graña ◽  
Nicolás Kovensky ◽  
Ander Retolaza
Keyword(s):  
Complex Geometry ◽  
Mass Term ◽  
Gaugino Mass ◽  
Generalized Complex

scholarly journals Blow-ups in generalized complex geometry

2018 ◽  
Vol 371 (3) ◽  
pp. 2109-2131
Author(s):  
M. A. Bailey ◽  
G. R. Cavalcanti ◽  
J. L. van der Leer Durán
Keyword(s):  
Complex Geometry ◽  
Generalized Complex

HERMITIAN COMPLEXITY OF REAL POLYNOMIAL IDEALS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250026 ◽  
Author(s):  
JOHN P. D'ANGELO ◽  
MIHAI PUTINAR
Keyword(s):  
Necessary Conditions ◽  
Complex Geometry ◽  
Polynomial Optimization ◽  
Symmetric Polynomial ◽  
Holomorphic Maps ◽  
Real Polynomial ◽  
Algebraic Subset ◽  
Algebraic Set ◽  
Holomorphic Embedding

We define the Hermitian complexity of a real polynomial ideal and of a real algebraic subset of Cn. This concept is aimed at determining precise necessary conditions for a Hermitian symmetric polynomial to agree with a Hermitian squared norm on an algebraic set. The latter topic has been a central theme in modern polynomial optimization and in complex geometry, specifically related to the holomorphic embedding of pseudoconvex domain into balls, or the classification of proper holomorphic maps between balls.

scholarly journals DIRAC BRACKETS FROM MAGNETIC BACKGROUNDS

2007 ◽  
Vol 04 (04) ◽  
pp. 523-532 ◽  
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Phase Space ◽  
Symplectic Form ◽  
Weak Magnetic Field ◽  
Complex Geometry ◽  
Poisson Brackets ◽  
Generalized Complex ◽  
Dirac Brackets ◽  
Classical Phase Space

In symplectic mechanics, the magnetic term describing the interaction between a charged particle and an external magnetic field has to be introduced by hand. On the contrary, in generalized complex geometry, such magnetic terms in the symplectic form arise naturally by means of B-transformations. Here we prove that, regarding classical phase space as a generalized complex manifold, the transformation law for the symplectic form under the action of a weak magnetic field gives rise to Dirac's prescription for Poisson brackets in the presence of constraints.

scholarly journals Courant algebroids and generalized complex geometry

2017 ◽  
Vol 47 (12) ◽  
pp. 1647-1664
Author(s):  
XU Ping ◽  
LIU ZhangJu ◽  
CHEN Zhuo
Keyword(s):  
Complex Geometry ◽  
Courant Algebroids ◽  
Generalized Complex

Geometry of String Theory Compactifications

2022 ◽  
Author(s):  
Alessandro Tomasiello
Keyword(s):  
Differential Geometry ◽  
String Theory ◽  
Complex Geometry ◽  
Einstein Manifolds ◽  
Special Holonomy ◽  
The Core ◽  
Mathematical Properties ◽  
Generalized Complex

String theory is a leading candidate for the unification of universal forces and matter, and one of its most striking predictions is the existence of small additional dimensions that have escaped detection so far. This book focuses on the geometry of these dimensions, beginning with the basics of the theory, the mathematical properties of spinors, and differential geometry. It further explores advanced techniques at the core of current research, such as G-structures and generalized complex geometry. Many significant classes of solutions to the theory's equations are studied in detail, from special holonomy and Sasaki–Einstein manifolds to their more recent generalizations involving fluxes for form fields. Various explicit examples are discussed, of interest to graduates and researchers.

scholarly journals AdS 5 Solutions of Type IIB Supergravity and Generalized Complex Geometry

2010 ◽  
Vol 299 (2) ◽  
pp. 365-408 ◽  
Author(s):  
Maxime Gabella ◽  
Jerome P. Gauntlett ◽  
Eran Palti ◽  
James Sparks ◽  
Daniel Waldram
Keyword(s):  
Complex Geometry ◽  
Generalized Complex
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