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

3 votes

Action of $\mathbb C^*$ on a closed orbit of a torus

In fact $X$ is a toric variety. "In general" the automorphism group of this variety is the torus himself. But in some cases it is not. For instance if $\varphi$ is the diagonal action of $\bf {C^*} ^n …
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  • 411
5 votes

Euler characteristic of a surface in $\mathbb{R}^3.$

You can assume that the $z$ function is Morse, compute the critical points (solve a Lagrange multiplier problem) and their indices (compute a second derivative), and remember that $\chi (S)= \sum _{c …
Thomas's user avatar
  • 411