论文标题
重言式交集数字的Ehrhart理论
An Ehrhart Theory For Tautological Intersection Numbers
论文作者
论文摘要
我们发现，$ \ bar {\ mathcal {m}} _ {g，n} $上的重言式交叉数，稳定的属属$ g $ curves的模uli空间，标记为$ n $，是对部分多型物体的ehrhart多项式的评估。为了证明这一点，我们将重言式相交数字的Virasoro限制因素作为整数值多项式的递归。然后，我们应用Breuer定理，该定理通过其$ f^*$ - 矢量的非负性分类，将部分多层复合物的Ehrhart多项式分类。在维度1和2中，我们表明出现的多面体复合物为\ emph {insion-Out polytopes}，即通过超平面布置解剖的多面体。
We discover that tautological intersection numbers on $\bar{\mathcal{M}}_{g, n}$, the moduli space of stable genus $g$ curves with $n$ marked points, are evaluations of Ehrhart polynomials of partial polytopal complexes. In order to prove this, we realize the Virasoro constraints for tautological intersection numbers as a recursion for integer-valued polynomials. Then we apply a theorem of Breuer that classifies Ehrhart polynomials of partial polytopal complexes by the nonnegativity of their $f^*$-vector. In dimensions 1 and 2, we show that the polytopal complexes that arise are \emph{inside-out polytopes} i.e. polytopes that are dissected by a hyperplane arrangement.
