Orbifold projective structures, differential operators, and logarithmic connections on a pointed Riemann surface. (English) Zbl 1106.32009
In this paper the author defines an orbifold projective structure on a compact Riemann surface with a given (finite) signature. This is a covering of the Riemann surface by an atlas with the appropriate ramification. In the definition given here the author remarks that the space of orbifold projective structures is an affine space over the space of quadratic differentials with at most simple poles and these on the support of the signature. An orbifold projective structure can be used to construct a holomorphic (logarithmic) connection on a certain bundle of 2-jets and the author characterises precisely which connection so arises. In the final section the author gives an alternative description of the space of orbifold projective structures using differential operators of order 3.
Reviewer: Samuel James Patterson (Göttingen)
MSC:
| 32C99 | Analytic spaces |
| 32C38 | Sheaves of differential operators and their modules, \(D\)-modules |
| 14F10 | Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials |
| 14H60 | Vector bundles on curves and their moduli |
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