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Everything about Complex projective space

Mathematical concept

In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space label the lines through the origin of a real Euclidean space, the points of a complex projective space label the complex lines through the origin of a complex Euclidean space (see below for an intuitive account). Formally, a complex projective space is the space of complex lines through the origin of an (n+1)-dimensional complex vector space. The space is denoted variously as P(Cn+1), Pn(C) or CPn. When n = 1, the complex projective space CP1 is the Riemann sphere, and when n = 2, CP2 is the complex projective plane (see there for a more elementary discussion). Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Complex projective spaceA 5-minute orientation
  2. Skim a recent paper: The string topology coproduct on complex and quaternionic projective spaceInfluential work since 2022
  3. Pick up a classic book: Vector bundles on complex projective spacesThe most-reprinted book on the subject
  4. Read the landmark paper: Real hypersurfaces and complex submanifolds in complex projective spaceCited 204 times
  5. Go sideways: Classifying space for U(n)A closely related topic
  6. Go sideways: Quaternionic projective spaceA closely related topic

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🗂️ The subject at a glance

  1. Introduction
  2. Construction
  3. Topology
  4. Differential geometry
  5. Algebraic geometry

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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