اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the Existence of Symplectic Resolutions of Symplectic Reductions
149
0
0.0
(
0
)
تأليف
Tanja Becker
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We compute the symplectic reductions for the action of Sp_2n on several copies of C^2n and for all coregular representations of Sl_2. If it exists we give at least one symplectic resolution for each example. In the case Sl_2 acting on sl_2+C^2 we obtain an explicit description of Fus and Namikawas example of two non-equivalent symplectic resolutions connected by a Mukai flop.
قيم البحث
اقرأ أيضاً
Recently, Herbig--Schwarz--Seaton have shown that $3$-large representations of a reductive group $G$ give rise to a large class of symplectic singularities via Hamiltonian reduction. We show that these singularities are always terminal. We show that
they are $mathbb{Q}$-factorial if and only if $G$ has finite abelianization. When $G$ is connected and semi-simple, we show they are actually locally factorial. As a consequence, the symplectic singularities do not admit symplectic resolutions when $G$ is semi-simple. We end with some open questions.
We introduce the notion of a conical symplectic variety, and show that any symplectic resolution of such a variety is isomorphic to the Springer resolution of a nilpotent orbit in a semisimple Lie algebra, composed with a linear projection.
We study the existence of symplectic resolutions of quotient singularities V/G where V is a symplectic vector space and G acts symplectically. Namely, we classify the symplectically irreducible and imprimitive groups, excluding those of the form $K r
times S_2$ where $K < SL_2(C)$, for which the corresponding quotient singularity admits a projective symplectic resolution. As a consequence, for $dim V eq 4$, we classify all quotient singularities $V/G$ admitting a projective symplectic resolution which do not decompose as a product of smaller-dimensional quotient singularities, except for at most four explicit singularities, that occur in dimensions at most 10, for whom the question of existence remains open.
In this article we consider the connected component of the identity of $G$-character varieties of compact Riemann surfaces of genus $g > 0$, for connected complex reductive groups $G$ of type $A$ (e.g., $SL_n$ and $GL_n$). We show that these varietie
s are symplectic singularities and classify which admit symplectic resolutions. The classification reduces to the semi-simple case, where we show that a resolution exists if and only if either $g=1$ and $G$ is a product of special linear groups of any rank and copies of the group $PGL_2$, or if $g=2$ and $G = (SL_2)^m$ for some $m$.
In this paper, we study the algebraic symplectic geometry of the singular moduli spaces of Higgs bundles of degree $0$ and rank $n$ on a compact Riemann surface $X$ of genus $g$. In particular, we prove that such moduli spaces are symplectic singular
ities, in the sense of Beauville [Bea00], and admit a projective symplectic resolution if and only if $g=1$ or $(g, n)=(2,2)$. These results are an application of a recent paper by Bellamy and Schedler [BS16] via the so-called Isosingularity Theorem.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
