complex geometry

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complex geometry

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complex geometry (uncountable)

1. (mathematics) The study of complex manifolds, complex algebraic varieties, and functions of several complex variables.

   Included in complex geometry are the application of transcendental methods to algebraic geometry, as well as the more geometric aspects of complex analysis.

   • 2004, Daniel Huybrechts, Complex Geometry: An Introduction, Springer, page vi:

     I tried to teach the subject in a way that would enable the students to follow recent developments in complex geometry and in particular some of the exciting aspects of the interplay between complex geometry and string theory.

   • 2004, Yum-Tong-Siu, Hyperbolicity in Complex Geometry, Olav Arnfinn Lauda, Ragni Piene (editors), The Legacy of Niels Henrik Abel, Springer, page 543,

     The hyperbolicity problem in complex geometry studies the conditions for a given complex manifold ${\displaystyle X}$ to be hyperbolic.

   • 2014, Robert S. Doran, Greg Friedman, Scott Nollet, Hodge Theory, Complex Geometry, and Representation Theory, American Mathematical Society, page ix:

     Professor Phillip Griffiths is a giant in complex geometry.

2. (countable) Used other than figuratively or idiomatically: see complex,‎ geometry.
   • 2013, Ahmed A. Shabana, Dynamics of Multibody Systems, Cambridge University Press, page 253:

     More discussion on the use of the parallel axis theorem in modeling the inertia of rigid bodies with complex geometry is presented in Chapter 8 of this book.