ترغب بنشر مسار تعليمي؟ اضغط هنا

Ginzburg algebras and the Hitchin connection for parabolic G-bundles

65   0   0.0 ( 0 )
 نشر من قبل Richard Wentworth
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

For a simple, simply connected, complex group G, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points.

قيم البحث

اقرأ أيضاً

Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people and they play an important role in higher Teichmuller theory. Geometric structures on a manifold a re closely related with representations of the fundamental group and with flat bundles. Higgs bundles can be very useful in describing flat bundles explicitly, via solutions of Hitchins equations. Baraglia has shown in his Ph.D. Thesis that Higgs bundles can also be used to construct geometric structures in some interesting cases. In this paper, we will explain the main ideas behind this theory and we will survey some recent results in this direction, which are joint work with Qiongling Li.
We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight system is generic. When the genus is at least two, using this result we also prove a Torelli theorem for the moduli space of semistable parabolic bundles of rank at least two with generic parabolic weights. The key input in the proofs is a method of J.C. Hurtubise, Integrable systems and algebraic surfaces, Duke Math. Jour. 83 (1996), 19--49.
We give an algebro-geometric construction of the Hitchin connection, valid also in positive characteristic (with a few exceptions). A key ingredient is a substitute for the Narasimhan-Atiyah-Bott Kahler form that realizes the Chern class of the deter minant-of-cohomology line bundle on the moduli space of bundles on a curve. As replacement we use an explicit realisation of the Atiyah class of this line bundle, based on the theory of the trace complex due to Beilinson-Schechtman and Bloch-Esnault.
128 - Emmanuel Letellier 2016
In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological interpretatio n for this counting using the moduli space of Higgs fields on the given vector bundle over the complex projective line with prescribed residues. We prove a certain number of results which bring evidences to the main conjecture. We detail the case of rank 2 vector bundles.
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