geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
(shape modality $\dashv$ flat modality $\dashv$ sharp modality)
$(\esh \dashv \flat \dashv \sharp )$
dR-shape modality$\dashv$ dR-flat modality
$\esh_{dR} \dashv \flat_{dR}$
(reduction modality $\dashv$ infinitesimal shape modality $\dashv$ infinitesimal flat modality)
$(\Re \dashv \Im \dashv \&)$
fermionic modality$\dashv$ bosonic modality $\dashv$ rheonomy modality
$(\rightrightarrows \dashv \rightsquigarrow \dashv Rh)$
Models
Models for Smooth Infinitesimal Analysis
smooth algebra ($C^\infty$-ring)
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
In complex geometry one studies complex manifolds as a special case of how in general differential geometry one studies more generally smooth manifolds.
In complex analytic geometry one studies, more generally, complex analytic spaces.
complex analytic geometry is closely related to algebraic geometry over the complex numbers. See at GAGA for more on this.
complex manifold, almost complex manifold
complex surface, complex curve
higher complex analytic geometry, derived complex analytic space
Daniel HuybrechtsComplex geometry - an introduction. Springer (2004). Universitext. 309 pages. (pdf)
Claire Voisin, Hodge theory and Complex algebraic geometry I,II, Cambridge Stud. in Adv. Math. 76, 77, 2002/3
Last revised on January 24, 2019 at 08:55:25. See the history of this page for a list of all contributions to it.