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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.

8 votes

Equivalence of derived categories which is not Fourier-Mukai

I don't know of a counterexample but I can tell you some more situations in which it is true. Ballard has extended Orlov's result (in Equivalences of derived categories of sheaves on quasi-projective …
David Roberts's user avatar
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Analogues of the Weierstrass p function for higher genus compact Riemann surfaces

In general the answer to 2) will be no since not every Riemann surface of genus >1 embeds into P^2 - the best one can do in general is find a curve birational to it with nodal singularities obtained b …
Greg Stevenson's user avatar