Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $k_4=Spec(k[x_1, x_2, x_3,x_4])$ and $\mathcal{I}$ is the ideal sheaf defined by $(x_1-x_2,x_3-x_4)$. Then

$$ Bl_{\mathcal{I}}(k^4) = Proj (\oplus_{i\geq 0} I^i t^i) $$ where $I=(x_1-x_2,x_3-x_4)$.

Then considering $Bl_{\mathcal{I}}(k^4)/S_2$ where $S_2$ is the symmetric group on $2$ letters, how do we write or see $$ Bl_{\mathcal{I}}(k^4)/S_2 $$ as $Proj$? The $S_2$ action on $Bl_{\mathcal{I}}(k^4)$ is by interchanging $(x_1,x_3)\in k^2$ with $(x_2, x_4)\in k^2$?

$$ $$

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.