{"title":"A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero","authors":"Jiayue Qi","doi":"10.1016/j.jsc.2023.102253","DOIUrl":null,"url":null,"abstract":"<div><p><span>The Chow ring of the moduli space of marked rational curves is generated by Keel's divisor classes. The top graded part of this Chow ring is isomorphic to the integers, generated by the class of a single point. In this paper, we give an equivalent graphical characterization on the monomials in this Chow ring, as well as the characterization on the algebraic reduction on such monomials. Moreover, we provide an algorithm for computing the intersection degree of tuples of Keel's divisor classes — we call it the forest algorithm; the complexity of which is </span><span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> in the worst case, where <em>n</em> refers to the number of marks in the ambient moduli space. Last but not least, we introduce three identities on multinomial coefficients which naturally came into play, showing that they are all equivalent to the correctness of the base case of the forest algorithm.</p></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"122 ","pages":"Article 102253"},"PeriodicalIF":0.6000,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symbolic Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0747717123000676","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
The Chow ring of the moduli space of marked rational curves is generated by Keel's divisor classes. The top graded part of this Chow ring is isomorphic to the integers, generated by the class of a single point. In this paper, we give an equivalent graphical characterization on the monomials in this Chow ring, as well as the characterization on the algebraic reduction on such monomials. Moreover, we provide an algorithm for computing the intersection degree of tuples of Keel's divisor classes — we call it the forest algorithm; the complexity of which is in the worst case, where n refers to the number of marks in the ambient moduli space. Last but not least, we introduce three identities on multinomial coefficients which naturally came into play, showing that they are all equivalent to the correctness of the base case of the forest algorithm.
期刊介绍：
An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects.
It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
