Theory of Multi-fans
نویسنده
چکیده
We introduce the notion of a multi-fan. It is a generalization of that of a fan in the theory of toric varieties in algebraic geometry. Roughly speaking a toric variety is an algebraic variety with an action of an algebraic torus of the same dimension as that of the variety, and a fan is a combinatorial object associated with the toric variety. Algebro-geometric properties of the toric variety can be described in terms of the associated fan. We develop a combinatorial theory of multi-fans and define “topological invariants” of a multi-fan. A smooth manifold with an action of a compact torus of half the dimension of the manifold and with some orientation data is called a torus manifold. We associate a unique multi-fan with a torus manifold, and apply the combinatorial theory to describe topological invariants of the torus manifold. A similar theory is also given for torus orbifolds. Though a multi-fan may correspond to more than one torus manifolds or orbifolds, it is shown that every complete simplicial multi-fan is assoiated with a certain torus orbifold. As a related subject a generalization of the Ehrhart polynomial concerning the number of lattice points in a convex polytope is discussed. The notion of multi-polytope generalizes that of convex polytope, and the number of lattice points in a multi-polytope is defined properly.
منابع مشابه
Elliptic Genera, Torus Orbifolds and Multi-fans
Multi-fan is an analogous notion of fan in toric theory. Fan is a combinatorial object associated to a toric variety. Multi-fan is associated to an orbifold with an action of half the dimension of the orbifold. In this paper the equivariant elliptic genus and the equivariant orbifold elliptic genus of multi-fans are defined and their character formulas are exhibited. A vanishing theorem concern...
متن کاملبررسی تأثیر ویژگی‌های هندسی حوضه‌ها در تشکیل مخروط‌افکنه‌های دامنه جنوبی البرز در استان سمنان با استفاده از روش‌های همبستگی و تحلیل سلسله مراتبی
Introduction Alluvial fans are considered as one of the arid and semi-arid geomorphic effects, which are the result of intense flow water performance in the past and present. Therefore, alluvial fans can be considered as legacies of quaternary climate. Dryv (1873) used alluvial fan terminology for the first time. The US geographical organization conducted a study focusing on alluvial fans in...
متن کاملElliptic Genera, Torus Orbifolds and Multi-fans; Ii
This article is a continuation of [HM2]. Elliptic genera for manifolds introduced by Ochanine and other people has a remarkable feature called rigidity. If the circle group acts non-trivially on a closed almost complex (or more generally stably almost complex) manifold whose first Chern class is divisible by a positive integer N greater than 1, then its equivariant elliptic genus of level N is ...
متن کاملModeling and Multi-Objective Optimization of Forward-Curved Blades Centrifugal Fans using CFD and Neural Networks
Increasing of head rise (HR) and decreasing of head loss (HL), simultaneously, are important purpose in the design of different types of fans. Therefore, multi-objective optimization process is more applicable for the design of such turbo machines. In the present study, multi-objective optimization of Forward-Curved (FC) blades centrifugal fans is performed at three steps. At the first step, He...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008