A note on the moduli spaces of holomorphic and logarithmic connections over a compact Riemann surface
نویسندگان
چکیده
Let X be a compact Riemann surface of genus $$g \ge 3$$ . We consider the moduli space holomorphic connections over and logarithmic singular finite subset with fixed residues. determine Chow group these spaces. compute global sections sheaves differential operators on ample line bundles their symmetric powers spaces show that they are constant under certain conditions. Torelli-type theorem for connections. also describe rational connectedness
منابع مشابه
TORELLI THEOREM FOR MODULI SPACES OF SL(r,C)–CONNECTIONS ON A COMPACT RIEMANN SURFACE
Let X be any compact connected Riemann surface of genus g, with g ≥ 3. For any r ≥ 2, let MX denote the moduli space of holomorphic SL(r, C)–connections over X . It is known that the biholomorphism class of the complex variety MX is independent of the complex structure of X . If g = 3, then we assume that r ≥ 3. We prove that the isomorphism class of the variety MX determines the Riemann surfac...
متن کاملThe Pontryagin rings of moduli spaces of arbitrary rank holomorphic bundles over a Riemann surface
The cohomology of M(n, d), the moduli space of stable holomorphic bundles of coprime rank n and degree d and fixed determinant, over a Riemann surface Σ of genus g ≥ 2, has been widely studied and from a wide range of approaches. Narasimhan and Seshadri [17] originally showed that the topology of M(n, d) depends only on the genus g rather than the complex structure of Σ. An inductive method to ...
متن کاملTorelli Theorem for the Moduli Spaces of Connections on a Riemann Surface
Let (X , x0) be any one–pointed compact connected Riemann surface of genus g, with g ≥ 3. Fix two mutually coprime integers r > 1 and d. Let MX denote the moduli space parametrizing all logarithmic SL(r, C)–connections, singular over x0, on vector bundles over X of degree d. We prove that the isomorphism class of the variety MX determines the Riemann surface X uniquely up to an isomorphism, alt...
متن کاملThe Hodge Numbers of the Moduli Spaces of Vector Bundles over a Riemann Surface
Let M(n, d) denote the moduli space of stable holomorphic vector bundles of coprime rank n and degree d over a fixed Riemann surface Σ of genus g ≥ 2. Let Λ be a fixed line bundle over Σ of degree d and let MΛ(n, d) ⊂ M(n, d) denote the space consisting of those bundles with determinant Λ. The spaces M(n, d) and MΛ(n, d) are nonsingular complex projective varieties whose geometry has been much ...
متن کاملAutomorphisms of C∗ Moduli Spaces Associated to a Riemann Surface
We compute the automorphism groups of the Dolbeault, de Rham and Betti moduli spaces for the multiplicative group C∗ associated to a compact connected Riemann surface.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Global Analysis and Geometry
سال: 2022
ISSN: ['1572-9060', '0232-704X']
DOI: https://doi.org/10.1007/s10455-022-09864-y