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What are hyperkähler metrics used for?

It seems that a lot of effort has been devoted to endow holomorphic-symplectic manifolds with hyperkähler metrics. It started with Calabi [4] with $T^*\mathbb{CP}^n$. Other examples include coadjoint ...
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8 votes
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Motivating derived stacks via Euclidean geometry

Here (see Section 3) triangles in Euclidean plane are used to motivate the notion of DM stack (an equilateral triangle has more symmetries than a generic triangle). Can something similar be done to ...
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6 votes
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Relative cohomology in algebraic topology vs algebraic geometry

There is a notion of relative cohomology in both algebraic topology and algebraic geometry and the flexibility granted by this relative viewpoint is quite powerful in both cases. However, the two ...
Asvin's user avatar
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