TOWARDS A CLASSIFICATION OF MODULAR COMPACTIFICATONS OF Mg,n
نویسنده
چکیده
The moduli space of smooth curves admits a beautiful compactification Mg,n ⊂ Mg,n by the moduli space of stable curves. In this paper, we undertake a systematic classification of alternate modular compactifications ofMg,n. Let Ug,n be the (non-separated) moduli stack of all n-pointed connected reduced one-dimensional schemes of arithmetic genus g. When g = 0, U0,n is irreducible and we classify all open proper substacks of U0,n. When g ≥ 1, Ug,n may not be irreducible, but there is a unique irreducible component Vg,n ⊂ Ug,n containing Mg,n. We classify open proper substacks of Vg,n satisfying a certain stability condition. Our classification gives an explicit link between the birational geometry of the universal curve C →Mg,n and the birational geometry ofMg,n. Indeed, every extremal face of the relative cone of curves of C → Mg,n gives rise to a modular compactification of Mg,n.
منابع مشابه
Development of Quality of Classroom Life Questionnaire in L2 Contexts: Investigating the Impact of Modular Instruction
Quality of Classroom Life is considered as a serious issue in academia around the world, and it has recently received global inquiry in EFL and ESL contexts. However, no questionnaire has been developed to assess the Iranian students’ and teachers’ attitudes towards the quality of life in the classroom. After developing a conceptual framework, the final draft of the developed questionnaire with...
متن کاملFixed points for Banach and Kannan contractions in modular spaces with a graph
In this paper, we discuss the existence and uniqueness of xed points for Banach and Kannancontractions dened on modular spaces endowed with a graph. We do not impose the Δ2-conditionor the Fatou property on the modular spaces to give generalizations of some recent results. Thegiven results play as a modular version of metric xed point results.
متن کاملModular approach for an ASIC integration of electrical drive controls
VLSI circuits design allows today to consider new modes of implementation for electrical controls. However, design techniques require an adaptation effort that few designers, too accustomed to the software approach, provide. The authors of this article propose to develop a methodology to guide the electrical designers towards optimal performances of control algorithms implementation. Thus, they...
متن کاملTotal Hip Arthroplasty with Modular Stem for Dysplastic Hips in South Asian Population
Introduction: Optimum component positioning and orientation is required to optimize the functional result during total hip arthroplasty for dysplastic hips. Patients and methods: Sixty-two patients (66 hips) including 33 males and 29 females underwent total hip arthroplasty using modular stem prosthesis at an average age of 40.6 years (range 17 to 49 years). Nineteen hips were clas...
متن کاملUsing Modular Pole for Multi-Objective Design Optimization of a Linear Permanent Magnet Synchronous Motor by Particle Swarm Optimization (PSO)
In this paper particle swarm optimization (PSO) is used for a design optimization of a linear permanent magnet synchronous motor (LPMSM) considering ultra low thrust force ripples, low magnet consumption, improved efficiency and thrust. The influence of PM material is discussed, too and the modular poles are proposed to achieve the best characteristic. PM dimensions and material, air gap and mo...
متن کامل