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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.
18
votes
1
answer
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Do all $\mathcal{N}=2$ Gauge Theories "Descend" from String Theory?
I asked this on PhysicsSE, but I think it also fits here as it's related to algebro-geometric connections to string and gauge theory.
I'm thinking about the beautiful story of "geometrical engineer …
7
votes
1
answer
427
views
Incorporating Divisors (D4-branes) into Donaldson-Thomas Theory?
Let $X$ be a Calabi-Yau threefold. Ordinary Donaldson-Thomas theory is formulated as a virtual count of ideal sheaves $\mathcal{I}$ with discrete invariants $\text{ch}(\mathcal{I}) = (1,0, -\beta, -n …
7
votes
2
answers
460
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Show Fiber Product of Rational Elliptic Surfaces is Calabi-Yau
In a handful of contexts people study Calabi-Yau threefolds formed by taking the fiber product of two rational elliptic surfaces. I can't find any detailed explanation of why such geometries are actu …
2
votes
0
answers
164
views
Chow variety of 1-cycles on abelian surface
It is an easy exercise to show that on a K3 surface, a smooth genus $g$ curve moves in a $g$-dimensional linear system. Nearly the same exercise shows that on an abelian surface, the corresponding li …