ترغب بنشر مسار تعليمي؟ اضغط هنا

Equivariant compactifications of vector groups with high index

136   0   0.0 ( 0 )
 نشر من قبل Pedro Montero
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this note, we classify smooth equivariant compactifications of $mathbb{G}_a^n$ which are Fano manifolds with index $geq n-2$.



قيم البحث

اقرأ أيضاً

131 - Daewoong Cheong 2016
Let $G$ be a simple complex algebraic group, $P$ a parabolic subgroup of $G$ and $N$ the unipotent radical of $P.$ The so-called equivariant compactification of $N$ by $G/P$ is given by an action of $N$ on $G/P$ with a dense open orbit isomorphic to $N$. In this article, we investigate how many such equivariant compactifications there exist. Our result says that there is a unique equivariant compactification of $N$ by $G/P$, up to isomorphism, except $P^n$.
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).
243 - Baohua Fu , Jun-Muk Hwang 2013
Let X be an $n$-dimensional Fano manifold of Picard number 1. We study how many different ways X can compactify the complex vector group C^n equivariantly. Hassett and Tschinkel showed that when X = P^n with n geq 2, there are many distinct ways that X can be realized as equivariant compactifications of C^n. Our result says that projective space is an exception: among Fano manifolds of Picard number 1 with smooth VMRT, projective space is the only one compactifying C^n equivariantly in more than one ways. This answers questions raised by Hassett-Tschinkel and Arzhantsev-Sharoyko.
Let $pi$ be a group equipped with an action of a second group $G$ by automorphisms. We define the equivariant cohomological dimension ${sf cd}_G(pi)$, the equivariant geometric dimension ${sf gd}_G(pi)$, and the equivariant Lusternik-Schnirelmann cat egory ${sf cat}_G(pi)$ in terms of the Bredon dimensions and classifying space of the family of subgroups of the semi-direct product $pirtimes G$ consisting of sub-conjugates of $G$. When $G$ is finite, we extend theorems of Eilenberg-Ganea and Stallings-Swan to the equivariant setting, thereby showing that all three invariants coincide (except for the possibility of a $G$-group $pi$ with ${sf cat}_G(pi)={sf cd}_G(pi)=2$ and ${sf gd}_G(pi)=3$). A main ingredient is the purely algebraic result that the cohomological dimension of any finite group with respect to any family of proper subgroups is greater than one. This implies a Stallings-Swan type result for families of subgroups which do not contain all finite subgroups.
For a local complete intersection morphism, we establish fiberwise denseness in the $n$-dimensional irreducible components of the compactification Nisnevich locally.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا