相关论文: Virtual Manifolds and Localization

We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a trivial bundle on a curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we reprove the…

We examine several currently used techniques for visualizing complex-valued functions applied to modular forms. We plot several examples and study the benefits and limitations of each technique. We then introduce a method of visualization…

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a…

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…

We show that mapping class groups associated to all types of real algebraic curves are virtual duality groups. We also deduce some results about the orbifold homotopy groups of the moduli spaces of real algebraic curves. We achieve these…

The problem of mathematical modeling in geography is one of the most important strategies in order to establish the evolution and the prevision of geographical phenomena. Models must have a simplified structure, to reflect essential…

Kawasaki's formula is a tool to compute holomorphic Euler characteristics of vector bundles on a compact orbifold X. Let X be an orbispace with perfect obstruction theory which admits an embedding in a smooth orbifold. One can then…

This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…

In the present work we intend to introduce a system based on VR (Virtual Reality) for examining analytical-geometric structures that occur in the study of mathematics and physics concepts in the last high school classes. In our opinion, an…

We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable pointed curves vanish away from strata corresponding to…

The virtual cohomology of an orbifold is a ring structure on the cohomology of the inertia orbifold whose product is defined via the pull-push formalism and the Euler class of the excess intersection bundle. In this paper we calculate the…

This paper constructs and studies the Gromov-Witten invariants and their properties for noncompact geometrically bounded symplectic manifolds. Two localization formulas for GW-invariants are also proposed and proved. As applications we get…

The complexity of the data generated by (magneto)-hydrodynamic (HD/MHD) simulations requires advanced tools for their analysis and visualization. The dramatic improvements in virtual reality (VR) technologies have inspired us to seek the…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing work to compute and visualize modular forms as 3D surfaces and…

Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…

This is the first part of a trilogy where we apply the theory of virtual manifold/orbifolds developed by the first named author and Tian to study the Gromov-Witten moduli spaces. In this paper, we resolve the main analytic issue arising…

The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy…