Corpus ID: 203736812

# A compactification of the moduli space of marked vertical lines in $\mathbb{C}^2$

@article{Bottman2019ACO,
title={A compactification of the moduli space of marked vertical lines in \$\mathbb\{C\}^2\$},
author={N. Bottman and A. Oblomkov},
journal={arXiv: Algebraic Geometry},
year={2019}
}
• Published 2019
• Mathematics
• arXiv: Algebraic Geometry
For $r \geq 1$ and $\mathbf{n} \in \mathbb{Z}_{\geq0}^r\setminus\{\mathbf{0}\}$, we construct a proper complex variety $\overline{2M}_{\mathbf{n}}$. $\overline{2M}_{\mathbf{n}}$ is locally toric, and it is equipped with a forgetful map $\overline{2M}_{\mathbf{n}} \to \overline M_{0,r+1}$. This space is a compactification of $2M_{\mathbf{n}}$, the configuration space of marked vertical lines in $\mathbb{C}^2$ up to translations and dilations. In the appendices, we give several examples and show… Expand
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#### References

SHOWING 1-9 OF 9 REFERENCES
Moduli spaces of witch curves topologically realize the 2-associahedra
For $r \geq 1$ and $\mathbf{n} \in \mathbb{Z}_{\geq0}^r\setminus\{\mathbf{0}\}$, we construct the compactified moduli space $\overline{2\mathcal{M}}_{\mathbf{n}}$ of witch curves of typeExpand
Pointed trees of projective spaces
• Mathematics
• 2005
We introduce a smooth projective variety $T_{d,n}$ which compactifies the space of configurations of $n$ distinct points on affine $d$-space modulo translation and homothety. The points in theExpand
Wonderful compactification of an arrangement of subvarieties
We define the wonderful compactification of an arrangement of subvarieties. Given a complex nonsingular algebraic variety $Y$ and certain collection $\mathcal{G}$ of subvarieties of $Y$, theExpand
Introduction to Toric Varieties.
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraicExpand
Binomial Ideals
• Mathematics
• 1994
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains manyExpand
Desingularization of toric and binomial varieties
• Mathematics
• 2004
We give a combinatorial algorithm for equivariant embedded resolution of singularities of a toric variety defined over a perfect field. The algorithm is realized by a finite succession of blowings-upExpand
Intersection theory of moduli space of stable N-pointed curves of genus zero
We give a new construction of the moduli space via a composition of smooth codimension two blowups and use our construction to determine the Chow ring
A version of Fulton – MacPherson compactification for pairs X → Y