Mathematical Gemstones
Young tableaux are to planes as labeled trees are to curves. Continuing from the previous post in this series, we introduce the Chow ring of $\overline{M}_{0,n}$ and some important classes. Recall that in the first post, we answered the question “How many cubic curves in $\mathbb{P}^3$ pass...
Mathematical Gemstones
Young tableaux are to planes as labeled trees are to curves. Continuing from the previous post in this series, we now show how to think of $\overline{M}_{0,n}$ as a projective variety. We now show how to look from the perspective of a single point, and combine this with the forgetting maps, to...
Mathematical Gemstones
Young tableaux are to planes as labeled trees are to curves. Continuing from the motivation of the previous post, we now dive into the structure of the moduli space $\overline{M}_{0,n}$, and construct two recursive structures that lead to beautiful inductive theory, and, in the next post, the...
Mathematical Gemstones
Young tableaux are to planes as labeled trees are to curves. This is the analogy from which I hope to start a series of posts on the beauty of the growing field of connections between the geometry of moduli spaces of curves, and combinatorics. What do the pictures above have in common? Two...
Mathematical Gemstones
I have written about the flag variety, the Springer resolution, and the relation between the type A Springer correspondence and Hall-Littlewood polynomials in a previous sequence of posts. Time to extend this construction to the (type A) affine flag variety, corresponding to affine Lie type...
Mathematical Gemstones
After a bit of a hiatus due to difficulties with Wordpress, Mathematical Gemstones is back! Feel free to browse the new layout. Today’s post introduces moduli spaces of curves, and one of the many ways combinatorial gemstones arise in this vast area of algebraic geometry. A brief motivating...