اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles
213
0
0.0
(
0
)
تأليف
Michael Lennox Wong
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we obtain parametrizations of the moduli space of principal bundles over a compact Riemann surface using spaces of Hecke modifications in several cases. We begin with a discussion of Hecke modifications for principal bundles and give constructions of universal Hecke modifications of a fixed bundle of fixed type. This is followed by an overview of the construction of the wonderful, or De Concini--Procesi, compactification of a semi-simple algebraic group of adjoint type. The compactification plays an important role in the deformation theory used in constructing the parametrizations. A general outline to construct parametrizations is given and verifications for specific structure groups are carried out.
قيم البحث
اقرأ أيضاً
Let G be a split reductive group. We introduce the moduli problem of bundle chains parametrizing framed principal G-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its moduli stack pr
ovides an equivariant toroidal compactification of G. All toric orbifolds may be thus obtained. Moreover, we get a canonical compactification of any semisimple G, which agrees with the wonderful compactification in the adjoint case, but which in other cases is an orbifold. Finally, we describe the connections with Losev-Manins spaces of weighted pointed curves and with Kauszs compactification of GL(n).
In this article, we solve the problem of constructing moduli spaces of semistable principal bundles (and singul
Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general point. As an
application, we show that X has the target rigidity property when G is not of type A_1 or C.
For a complex connected semisimple linear algebraic group G of adjoint type and of rank n, De Concini and Procesi constructed its wonderful compactification bar{G}, which is a smooth Fano G times G-variety of Picard number n enjoying many interesting
properties. In this paper, it is shown that the wonderful compactification bar{G} is rigid under Fano deformations. Namely, for any family of smooth Fano varieties over a connected base, if one fiber is isomorphic to bar{G}, then so are all other fibers.
In this note, we introduce the notion of a singular principal G-bundle, associated to a reductive algebraic group G over the complex numbers by means of a faithful representation $varrho^pcolon Glra SL(V)$. This concept is meant to provide an analogo
n to the notion of a torsion free sheaf as a generalization of the notion of a vector bundle. We will construct moduli spaces for these singular principal bundles which compactify the moduli spaces of stable principal bundles.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
