اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRecent developments in toric geometry
58
0
0.0
(
0
)
تأليف
David A. Cox
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic geometry, combinatorics and mirror symmetry.
قيم البحث
اقرأ أيضاً
This expository survey is based on my online talk at the ICCM 2020. It aims to sketch key steps of the recent proof of the uniform Mordell-Lang conjecture for curves embedded into Jacobians (a question of Mazur). The full version of this conjecture i
s proved by combining Dimitrov-Gao-Habegger (https://annals.math.princeton.edu/articles/17715) and K{u}hne (arXiv:2101.10272). We include in this survey a detailed proof on how to combine these two results, which was implicitly done in another short paper of Dimitrov-Gao-Habegger (arXiv:2009.08505) but not explicitly written in existing literature. At the end of the survey we state some future aspects.
We study deformations of affine toric varieties. The entire deformation theory of these singularities is encoded by the so-called versal deformation. The main goal of our paper is to construct the homogeneous part of some degree -R of this, i.e. a ma
ximal deformation with prescribed tangent space T^1(-R) for a given character R. To this aim we use the polyhedron obtained by cutting the rational cone defining the affine singularity with the hyperplane defined by [R=1]. Under some length assumptions on the edges of this polyhedron, we provide the versal deformation for primitive degrees R.
In this review an overview on some recent developments in deformation quantization is given. After a general historical overview we motivate the basic definitions of star products and their equivalences both from a mathematical and a physical point o
f view. Then we focus on two topics: the Morita classification of star product algebras and convergence issues which lead to the nuclear Weyl algebra.
This is a survey on recent developments in Ricci flows.
Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The second dea
ls with generic oscillatory singularities in inhomogeneous cosmologies, especially those with two commuting spacelike Killing vectors. This paper describes recent progress in these two areas: in the spatially homogeneous case focus is on mathematically rigorous results, while analytical and numerical results concerning generic behavior and so-called recurring spike formation are the main topic in the inhomogeneous case. Unifying themes are connections between asymptotic behavior, hierarchical structures, and solution generating techniques, which provide hints for a link between the nature of generic singularities and a hierarchy of hidden asymptotic symmetries.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
