اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHodge polynomials of the moduli spaces of rank 3 pairs
153
0
0.0
(
0
)
تأليف
Vicente Mu~noz
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $X$ be a smooth projective curve of genus $ggeq 2$ over the complex numbers. A holomorphic triple $(E_1,E_2,phi)$ on $X$ consists of two holomorphic vector bundles $E_1$ and $E_2$ over $X$ and a holomorphic map $phi:E_2 to E_1$. There is a concept of stability for triples which depends on a real parameter $sigma$. In this paper, we determine the Hodge polynomials of the moduli spaces of $sigma$-stable triples with $rk(E_1)=3$, $rk(E_2)=1$, using the theory of mixed Hodge structures. This gives in particular the Poincare polynomials of these moduli spaces. As a byproduct, we recover the Hodge polynomial of the moduli space of odd degree rank 3 stable vector bundles.
قيم البحث
اقرأ أيضاً
Let $X$ be a compact Riemann surface $X$ of genus at--least two. Fix a holomorphic line bundle $L$ over $X$. Let $mathcal M$ be the moduli space of Hitchin pairs $(E ,phiin H^0(End(E)otimes L))$ over $X$ of rank $r$ and fixed determinant of degree $d
$. We prove that, for some numerical conditions, $mathcal M$ is irreducible, and that the isomorphism class of the variety $mathcal M$ uniquely determines the isomorphism class of the Riemann surface $X$.
We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.
We describe new components of the Gieseker--Maruyama moduli scheme $mathcal{M}(n)$ of semistable rank 2 sheaves $E$ on $mathbb{P}^3$ with $c_1(E)=0$, $c_2(E)=n$ and $c_3(E)=0$ whose generic point corresponds to non locally free sheaves. We show that
such components grow in number as $n$ grows, and discuss how they intersect the instanton component. As an application, we prove that $mathcal{M}(2)$ is connected, and identify a connected subscheme of $mathcal{M}(3)$ consisting of 7 irreducible components.
We prove formulas for the rational Chow motives of moduli spaces of semistable vector bundles and Higgs bundles of rank 3 and coprime degree on a smooth projective curve. Our approach involves identifying criteria to lift identities in (a completion
of) the Grothendieck group of effective Chow motives to isomorphisms in the category of Chow motives. For the Higgs moduli space, we use motivic Bialynicki-Birula decompositions associated to a scaling action with variation of stability and wall-crossing for moduli spaces of rank 2 pairs, which occur in the fixed locus of this action.
We study the irreducible components of the moduli space of instanton sheaves on $mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with $c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In particular, we classify all instanton sheaves with
$c_2(E)le4$, describing all the irreducible components of their moduli space. A key ingredient for our argument is the study of the moduli space ${mathcal T}(d)$ of stable sheaves on $mathbb{P}^3$ with Hilbert polynomial $P(t)=dcdot t$, which contains, as an open subset, the moduli space of rank 0 instanton sheaves of multiplicity $d$; we describe all the irreducible components of ${mathcal T}(d)$ for $dle4$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
