Take the 2-minute tour ×  What is 'Transcendental algebraic
geometry'? Could you give me some good references in this field?
Thanks.  share|improve this question add comment  3 Answers  up
vote 9 down vote accepted  Transcendental Algebraic Geometry is
the study of the algebraic geometry of a variety defined over
the complex numbers $\mathbb C$ by concentrating on its
undelying structure as a holomorphic manifold or variety. This
allows one to study the variety through the powerful tools of
topology, analysis and differential geometry like :
characteristic classes, elliptic partial differential equations,
Kähler structure, ... Serre wrote a remarkable article (always
quoted as GAGA!) giving a very precise functorial correspondence
between a projective algebraic variety $X$ over $\mathbb C$ and
the corresponding complex analytic variety $X^{an}$: here it is.
Voisin's book mentioned by sweetjazz is indeed masterful but
rather advanced. Two good introductory, fairly reader friendly,
books to that area are Taylo