Nate Bottman
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Registered User
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Grad student at MIT studying symplectic geometry.
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May 13 |
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Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety? @David I agree you can get all the Betti numbers except in the middle dimension (and that too, if you can get the Euler characteristic). But does this say much about the ring structure? |
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May 12 |
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Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety? OK, thanks Mariano. I find it really surprising that the ring structure of a projective hypersurface isn't easy to compute! |
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May 11 |
revised |
Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety? added 10 characters in body; added 81 characters in body |
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May 11 |
asked | Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety? |
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May 7 |
awarded | ● Teacher |
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Apr 30 |
awarded | ● Enthusiast |
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Apr 20 |
answered | Square root for Hamiltonian diffeomorphisms |
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Apr 13 |
revised |
What is known about the strong Arnold conjecture? added 767 characters in body |
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Apr 12 |
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A question on the SYZ mirror symmetry In "Mirror symmetry and T-duality in the complement of an anticanonical divisor", Denis Auroux works a number of examples of SYZ for Fano varieties. The toric Fano case is a good starting point: everything is totally concrete and geometric. (An unrelated reason to read that paper is that it's the only place I know of where the folk theorem that the self-Floer cohomology of a Lagrangian is a module over quantum cohomology is written down.) |
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Apr 12 |
asked | What is known about the strong Arnold conjecture? |
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Apr 12 |
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Fixed point theorems (the Hamiltonian and the function had better be nondegenerate) |
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Apr 8 |
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Homology classes represented by $J$-holomorphic curves For the record, as long as $\Sigma$ is closed and $(M,J,\omega)$ is almost-Kaehler the reason that $u_*[\Sigma]$ can't be torsion is the energy identity. |
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Mar 9 |
awarded | ● Supporter |
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Mar 8 |
awarded | ● Scholar |
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Mar 8 |
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How many “elementary” characterizations of twisted SU(2) representation varieties are known? Thanks Sam! This is so cool. Can someone with enough rep change $\mathbb{P}^{2g+2}$ to $\mathbb{P}^{2g+1}$? Here's how you get the two quadrics in $\mathbb{P}^{2g+1}$: let $\Sigma_g$ double-cover $\mathbb{P}^1$ with branch points $\lambda_0, \ldots, \lambda_{2g+1}$. Then the two quadrics are cut out by $X_0^2 + \cdots + X_{2g+1}^2$ and $\lambda_0X_0^2 + \cdots + \lambda_{2g+1}X_{2g+1}^2$. |
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Feb 25 |
revised |
How many “elementary” characterizations of twisted SU(2) representation varieties are known? added 5 characters in body |
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Feb 24 |
awarded | ● Autobiographer |
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Feb 24 |
awarded | ● Student |
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Feb 24 |
awarded | ● Editor |
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Feb 24 |
revised |
How many “elementary” characterizations of twisted SU(2) representation varieties are known? added 79 characters in body |
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Feb 24 |
asked | How many “elementary” characterizations of twisted SU(2) representation varieties are known? |
