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- W2996953921 abstract "The moduli space $overline{M}_{0,n}$ may be embedded into the product of projective spaces $mathbb{P}^1times mathbb{P}^2times cdots times mathbb{P}^{n-3}$, using a combination of the Kapranov map $|psi_n|:overline{M}_{0,n}to mathbb{P}^{n-3}$ and the forgetful maps $pi_i:overline{M}_{0,i}to overline{M}_{0,i-1}$. We give an explicit combinatorial formula for the multidegree of this embedding in terms of certain parking functions of height $n-3$. We use this combinatorial interpretation to show that the total degree of the embedding (thought of as the projectivization of its cone in $mathbb{A}^2times mathbb{A}^3cdots times mathbb{A}^{n-2}$) is equal to $(2(n-3)-1)!!=(2n-7)(2n-9) cdots(5)(3)(1)$. As a consequence, we also obtain a new combinatorial interpretation for the odd double factorial." @default.
- W2996953921 created "2020-01-10" @default.
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- W2996953921 date "2019-12-27" @default.
- W2996953921 modified "2023-09-27" @default.
- W2996953921 title "Projective Embeddings of $overline{M}_{0,n}$ and Parking Functions" @default.
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