Algebraic Constructions of Minimal Compactifications

2013 ◽  
Author(s):  
Kai-Wen Lan
Keyword(s):  
Large Class ◽  
Automorphic Forms ◽  
Algebraic Construction ◽  
Local Structures ◽  
Jacobi Expansion ◽  
Integral Bases ◽  
Toroidal Compactifications ◽  
Jacobi Expansions ◽  
Algebraic Constructions ◽  
Moduli Problems

This chapter first studies the automorphic forms that are defined as global sections of certain invertible sheaves on the toroidal compactifications. The local structures of toroidal compactifications lead naturally to the theory of Fourier–Jacobi expansions and the Fourier–Jacobi expansion principle. The chapter also obtains the algebraic construction of arithmetic minimal compactifications (of the coarse moduli associated with moduli problems), which are projective normal schemes defined over the same integral bases as the moduli problems are. As a by-product of codimension counting, we obtain Koecher's principle for arithmetic automorphic forms (of naive parallel weights). Furthermore, this chapter shows the projectivity of a large class of arithmetic toroidal compactifications by realizing them as normalizations of blowups of the corresponding minimal compactifications.

Algebraic Constructions of Toroidal Compactifications

2013 ◽  
Author(s):  
Kai-Wen Lan
Keyword(s):  
General Construction ◽  
Formal Models ◽  
Algebraic Models ◽  
Algebraic Construction ◽  
Algebraic Stacks ◽  
Local Structures ◽  
Correct Formulation ◽  
Toroidal Compactifications ◽  
Multiplicative Type ◽  
Algebraic Constructions

This chapter explains the algebraic construction of toroidal compactifications. For this purpose the chapter utilizes the theory of toroidal embeddings for torsors under groups of multiplicative type. Based on this theory, the chapter begins the general construction of local charts on which degeneration data for PEL structures are tautologically associated. The next important step is the description of good formal models, and good algebraic models approximating them. The correct formulation of necessary properties and the actual construction of these good algebraic models are the key to the gluing process in the étale topology. In particular, this includes the comparison of local structures using certain Kodaira–Spencer morphisms. As a result of gluing, this chapter obtains the arithmetic toroidal compactifications in the category of algebraic stacks. The chapter is concluded by a study of Hecke actions on towers of arithmetic toroidal compactifications.

QUANTUM SYMMETRIES OF STRING VACUA

1989 ◽  
Vol 04 (17) ◽  
pp. 1615-1626 ◽  
Author(s):  
CUMRUN VAFA
Keyword(s):  
Global Symmetries ◽  
Large Class ◽  
Moduli Space ◽  
Quantum Level ◽  
Present Evidence ◽  
Toroidal Compactifications ◽  
Quantum Symmetries ◽  
Underlying Manifold

We show that for a large class of string vacua, by a proper tuning of the metric (and the axionic fields), one obtains global symmetries. Moreover, the string vacua which arise as orbifoldized Landau-Ginzburg models are equipped with precisely this metric. These symmetries are not symmetries of the underlying manifold, rather they are symmetries of the superconformal theory manifest only at the Quantum level. These generalize the duality symmetries well known for toroidal compactifications, to a large class of string vacua. Moreover we discuss in detail the global symmetries of the quantum K3 space, and present evidence that the global symmetries of the moduli space of this theory is SO (20, 4; Z).

A Large Class of p-Ary Cyclic Codes and Sequence Families

2010 ◽  
Vol E93-A (11) ◽  
pp. 2272-2277
Author(s):  
Zhengchun ZHOU ◽  
Xiaohu TANG ◽  
Udaya PARAMPALLI
Keyword(s):  
Large Class ◽  
Cyclic Codes

Single Image Dehazing by Predicting Atmospheric Scattering Parameters

2020 ◽  
Vol 2020 (1) ◽  
pp. 74-77
Author(s):  
Simone Bianco ◽  
Luigi Celona ◽  
Flavio Piccoli
Keyword(s):  
Reference Image ◽  
Single Image ◽  
Scattering Parameters ◽  
Image Dehazing ◽  
Atmospheric Scattering ◽  
Local Structures ◽  
Full Reference ◽  
Reconstruction Quality ◽  
Single Image Dehazing

In this work we propose a method for single image dehazing that exploits a physical model to recover the haze-free image by estimating the atmospheric scattering parameters. Cycle consistency is used to further improve the reconstruction quality of local structures and objects in the scene as well. Experimental results on four real and synthetic hazy image datasets show the effectiveness of the proposed method in terms of two commonly used full-reference image quality metrics.

The Social Furniture of Virtual Worlds

Disputatio ◽  
2019 ◽  
Vol 11 (55) ◽  
pp. 345-369
Author(s):  
Peter Ludlow
Keyword(s):  
Large Class ◽  
Data Structures ◽  
Virtual Worlds ◽  
Causal Powers ◽  
Virtual Objects ◽  
David Chalmers ◽  
The Social

AbstractDavid Chalmers argues that virtual objects exist in the form of data structures that have causal powers. I argue that there is a large class of virtual objects that are social objects and that do not depend upon data structures for their existence. I also argue that data structures are themselves fundamentally social objects. Thus, virtual objects are fundamentally social objects.

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