ترغب بنشر مسار تعليمي؟ اضغط هنا

Geometric Quantization of the moduli space of the vortex equations on a Riemann surface

164   0   0.0 ( 0 )
 نشر من قبل Rukmini Dey Dr.
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English
 تأليف Rukmini Dey




اسأل ChatGPT حول البحث

In this note we quantize the usual symplectic (K{a}hler) form on the vortex moduli space by modifying the Quillen metric of the Quillen determinant line bundle.

قيم البحث

اقرأ أيضاً

181 - Rukmini Dey 2016
This paper is about geometric quantization of the Hitchin system. We quantize a Kahler form on the Hitchin moduli space (which is half the first Kahler form defined by Hitchin) by considering the Quillen bundle as the prequantum line bundle and modif ying the Quillen metric using the Higgs field so that the curvature is proportional to the Kahler form. We show that this Kahler form is integral and the Quillen bundle descends as a prequantum line bundle on the moduli space. It is holomorphic and hence one can take holomorphic square integrable sections as the Hilbert space of quantization of the Hitchin moduli space.
In this paper, the moduli space of singular unitary Hermitian--Einstein monopoles on the product of a circle and a Riemann surface is shown to correspond to a moduli space of stable pairs on the Riemann surface. These pairs consist of a holomorphic v ector bundle on the surface and a meromorphic automorphism of the bundle. The singularities of this automorphism correspond to the singularities of the singular monopole. We then consider the complex geometry of the moduli space; in particular, we compute dimensions, both from the complex geometric and the gauge theoretic point of view.
119 - Indranil Biswas 2021
Let X be a compact connected Riemann surface of genus g > 0 equipped with a nonzero holomorphic 1-form. Let M denote the moduli space of semistable Higgs bundles on X of rank r and degree r(g-1)+1; it is a complex symplectic manifold. Using the trans lation structure on the open subset of X where the 1-form does not vanish, we construct a natural deformation quantization of a certain nonempty Zariski open subset of M.
We describe some results on moduli space of logarithmic connections equipped with framings on a $n$-pointed compact Riemann surface.
181 - Yuuji Tanaka 2016
In alignment with a programme by Donaldson and Thomas [DT], Thomas [Th] constructed a deformation invariant for smooth projective Calabi-Yau threefolds, which is now called the Donaldson-Thomas invariant, from the moduli space of (semi-)stable sheave s by using algebraic geometry techniques. In the same paper [Th], Thomas noted that certain perturbed Hermitian-Einstein equations might possibly produce an analytic theory of the invariant. This article sets up the equations on symplectic 6-manifolds, and gives the local model and structures of the moduli space coming from the equations. We then describe a Hitchin-Kobayashi style correspondence for the equations on compact Kahler threefolds, which turns out to be a special case of results by Alvarez-Consul and Garcia-Prada [AG].
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