Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 152 / 1 / a / i

Table of contents
- Solution i

Solution

For

m = (u, v) \in M ≅ Z^{2}

, membership in the dual cone is equivalent to

u \geq 0, - u + 3 v \geq 0.

The Hilbert basis of a rational cone is

(0, 1), (1, 1), (2, 1), (3, 1)

. Therefore the coordinate ring of an affine toric variety is

C [S_{σ}] = C [t_{2}, t_{1} t_{2}, t_{1}^{2} t_{2}, t_{1}^{3} t_{2}] \subseteq C [t_{1}^{\pm 1}, t_{2}^{\pm 1}] .

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version