Projective embeddings of (M)over-bar0,n and parking functions

被引：1
|
作者：
Cavalieri, Renzo
Gillespie, Maria
Monin, Leonid
机构：
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2021年 / 182卷
基金：
英国工程与自然科学研究理事会;
关键词：
Parking functions; Moduli of curves; Multidegree; Intersection theory; POINTED CURVES; MODULI SPACES;
D O I：
10.1016/j.jcta.2021.105471
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The moduli space (M) over bar (0,)n may be embedded into the product of projective spaces P-1 xP(2) x center dot center dot center dot xP(n-3), using a combination of the Kapranov map vertical bar psi(n vertical bar) : (M) over bar (0,)n -> Pn-3 and the forgetful maps pi(i): (M) over bar (0,i) -> (M) over bar (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 A(2) x A(3) center dot center dot center dot x A(n-2)) is equal to (2( n - 3) - 1)!! = (2n - 7)(2n - 9) center dot center dot center dot (5)(3)(1). As a consequence, we also obtain a new combinatorial interpretation for the odd double factorial. (C) 2021 Elsevier Inc. All rights reserved.
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页数：30
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