Timeline for Geometric interpretation of algebraic tangent cone
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2018 at 11:28 | vote | accept | Mohan Swaminathan | ||
| Mar 16, 2018 at 15:44 | answer | added | Eric Canton | timeline score: 5 | |
| Mar 15, 2018 at 18:44 | comment | added | Jason Starr | If $(A,\mathfrak{m})$ is the germ of a $k$-scheme $(X,x)$, then form the product $X\times \text{Spec} \ k[[t]]$ with its projection to the DVR $\text{Spec}\ k[[t]]$. Next, blow this up at the point $x$ in the closed fiber, $\nu:\mathcal{X} \to X\times \text{Spec}\ k[[t]]$. Every formal arc of $X$ centered at $x$ gives a section of the projection, which then lifts uniquely to $\mathcal{X}$ by the valuative criterion applied to $\nu$. The fiber of $\nu$ over $x$ is the (projective completion) of the algebraic tangent cone, cf. "deformation to the normal cone". | |
| Mar 15, 2018 at 18:16 | history | asked | Mohan Swaminathan | CC BY-SA 3.0 |