This can make toric kinds a very eye-catching check circumstance For lots of constructions in complex geometry. Examples of toric versions incorporate complex projective spaces, and bundles in excess of them.
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complex variables. To outline a projective complex algebraic selection, a single demands the subset X ⊆ C P n displaystyle Xsubseteq mathbb CP ^ n
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Complex geometry also will make use of methods arising from differential geometry and Evaluation. By way of example, the Hirzebruch-Riemann-Roch theorem, a Distinctive circumstance from the Atiyah-Singer index theorem, computes the holomorphic Euler characteristic of a holomorphic vector bundle concerning characteristic courses with the fundamental smooth complex vector bundle.