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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
3
votes
Good overview of singularity theory
There is the classic Singular Points of Complex Hypersurfaces by J. W. Milnor. Try also Topics in real and complex singularities by A. Dimca.
8
votes
Derived categories of toric varieties and convex geometry
That's a great question!
In the last few years there is plenty of research on the subject - and a few (interesting) open questions.
Before Kawamta's result - note that toric manifolds satisfy $rk( …