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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

2 votes
2 answers
485 views

Nontrivial Analytic Varieties

In short, I'd like to know the following: Is there an irreducible analytic variety that has to be defined by at least two distinct sets of holomorphic functions? Are there two irreducible analytic v …
finnlim's user avatar
  • 517
37 votes
6 answers
6k views

Why study Higher Sheaf Cohomology?

The classical lore is that $H^1(X,\mathcal F)$ is obstruction to lifting local data to global data. However I don't understand why one would want to compute $H^3(X,\mathcal F), H^4(X,\mathcal F), \cdo …
finnlim's user avatar
  • 517