Related papers: GIT Compactifications of $M_{0,n}$ from Conics

We associate real and regular algebraic--geometric data to each multi--line soliton solution of Kadomtsev-Petviashvili II (KP) equation. These solutions are known to be parametrized by points of the totally non--negative part of real…

The literature on maximal torus orbits in the Grassmannian is vast; in this paper we initiate a program to extend this to diagonal subtori. Our main focus is generalizing portions of Kapranov's seminal work on Chow quotient…

We describe the GIT compactification for the moduli space of smooth quintic surfaces in projective space. In particular, we show that a normal quintic surface with at worst an isolated double point or a minimal elliptic singularity is…

We compute the Poincar\'e polynomials of the compactified Jacobians for plane curve singularities with Puiseaux exponents $(nd,md,md+1)$, and relate them to the combinatorics of $q,t$-Catalan numbers in the non-coprime case. We also confirm…

Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic…

Bosio generalized the construction by Meersseman of a family of non-algebraic compact complex manifolds of any dimension. We establish a link between Bosio's construction and GIT quotients. We show that his generalization parallels exactly…

This paper generalizes the fundamental GAGA results of Serre cite{MR0082175} in three ways---to the non-separated setting, to stacks, and to families. As an application of these results, we show that analytic compactifications of…

We present a general framework for Matrix theory compactified on a quotient space R^n/G, with G a discrete group of Euclidean motions in R^n. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We…

We study the moduli space of M-theories compactified on G_2 manifolds which are asymptotic to a cone over quotients of S^3 x S^3. We show that the moduli space is composed of several components, each of which interpolates smoothly among…

We study the GIT quotients for the diagonal action of the algebraic group $SL_3(\mathbb{C})$ on the $n$-fold product of $\mathbb{P}^2(\mathbb{C})$: in particular we determine a strategy in order to determine the (intersection) Poincar\'{e}…

We perform a variation of geometric invariant theory stability analysis for 2nd Hilbert points of bi-log-canonically embedded pointed curves of genus two. As a result, we give a GIT construction of the last three non-trivial log canonical…

Let $ G = \mathbb{Z}/r\mathbb{Z}$ be the cyclic group of order $r$, and let $\varpi = e^{2\pi i / r}$ denote a primitive $r$ th root of unity. Consider the action of $G$ on $\mathbb{C}^n$ via the embedding $$ \varphi : G \hookrightarrow…

The generalized Petersen graph $G(n, k)$ is a cubic graph with vertex set $V(G(n, k)) = \{v_i\}_{0 \leq i < n} \cup \{w_i\}_{0 \leq i < n}$ and edge set $E(G(n, k)) = \{v_i v_{i+1}\}_{0 \leq i < n} \cup \{w_i w_{i+k}\}_{0 \leq i < n} \cup…

Motivated by Stanley's generalization of the chromatic polynomial of a graph to the chromatic symmetric function, we introduce the characteristic polynomial of a representation of the symmetric group, or more generally, of a symmetric…

The goal of this text is to understand and prove a formula stated by Salmon, which gives the first terms of some Taylor expansion of the discriminant of a plane algebraic curve. Salmon uses his formula to derive various enumerative…

This largely expository paper first gives an introduction to Hilbert stability and its use in Gieseker's GIT construction of $\overline{M}_g$. Then I review recent work in this area--variants for unpointed curves that arise in Hassett's log…

We prove that the Losev--Manin compactification of the space of configurations of $n$ points on ${\mathbb P}^1 \backslash \{0,\infty\}$ modulo scaling degenerates (isotrivially) to a compactification of the space of configurations of $n$…

The general solution of the graded contraction equations for a $\zz_2^{\otimes N}$ grading of the real compact simple Lie algebra $so(N+1)$ is presented in an explicit way. It turns out to depend on $2^N-1$ independent real parameters. The…

For a finite subgroup $\Gamma\subset \mathrm{SL}(2,\mathbb{C})$ and for $n\geq 1$, we use variation of GIT quotient for Nakajima quiver varieties to study the birational geometry of the Hilbert scheme of $n$ points on the minimal resolution…

We describe a formalism based on quantization of quadratic hamiltonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about Gromov-Witten invariants of compact…