On the Mathematics and Physics of High Genus Invariants
نویسنده
چکیده
This paper wishes to foster communication between mathematicians and physicists working in mirror symmetry and orbifold Gromov-Witten theory. We provide a reader friendly review of the physics computation in [ABK06] that predicts Gromov-Witten invariants of [C/Z3] in arbitrary genus, and of the mathematical framework for expressing these invariants as Hodge integrals. Using geometric properties of the Hodge classes, we compute the unpointed invariants for g = 2, 3, thus providing the first high genus mathematical check of the physics predictions.
منابع مشابه
New Algorithm For Computing Secondary Invariants of Invariant Rings of Monomial Groups
In this paper, a new algorithm for computing secondary invariants of invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants. The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...
متن کاملOn the M-polynomial of planar chemical graphs
Let $G$ be a graph and let $m_{i,j}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The $M$-polynomial of $G$ is $M(G;x,y) = sum_{ile j} m_{i,j}(G)x^iy^j$. With $M(G;x,y)$ in hands, numerous degree-based topological indices of $G$ can be routinely computed. In this note a formula for the $M$-polynomial of planar (chemical) graphs which have only vertices...
متن کاملOn leap Zagreb indices of graphs
The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established.
متن کاملOptimization of Imaging Parameters in Micro-CT Scanner Based On Signal-To-Noise Ratio for the Analysis of Urinary Stone Composition
Introduction: Micro-CT scanner with a resolution of about 5 micrometers is one of the modalities used to create three-dimensional/two-dimensional images of urinary stones. This study aimed to optimize imaging parameters in micro-computed tomography (CT) scanner based on the signal-to-noise ratio (SNR) of urinary stones for the analysis of stone composition. <stro...
متن کاملChemical Trees with Extreme Values of Zagreb Indices and Coindices
We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.
متن کامل