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- W4302558218 abstract "We study enumerative questions on the moduli space $mathcal{M}(L)$ of hyperplane arrangements with a given intersection lattice $L$. Mnev's universality theorem suggests that these moduli spaces can be arbitrarily complicated; indeed it is even difficult to compute the dimension $D =dim mathcal{M}(L)$. Embedding $mathcal{M}(L)$ in a product of projective spaces, we study the degree $N=mathrm{deg} mathcal{M}(L)$, which can be interpreted as the number of arrangements in $mathcal{M}(L)$ that pass through $D$ points in general position. For generic arrangements $N$ can be computed combinatorially and this number also appears in the study of the Chow variety of zero dimensional cycles. We compute $D$ and $N$ using Schubert calculus in the case where $L$ is the intersection lattice of the arrangement obtained by taking multiple cones over a generic arrangement. We also calculate the characteristic numbers for families of generic arrangements in $mathbb{P}^2$ with 3 and 4 lines." @default.
- W4302558218 created "2022-10-06" @default.
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- W4302558218 date "2014-09-22" @default.
- W4302558218 modified "2023-10-16" @default.
- W4302558218 title "The Enumerative Geometry of Hyperplane Arrangements" @default.
- W4302558218 doi "https://doi.org/10.48550/arxiv.1409.6275" @default.
- W4302558218 hasPublicationYear "2014" @default.
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