Titlebook: Geometry of Algebraic Curves; Volume II with a con Enrico Arbarello,Maurizio Cornalba,Phillip A. Grif Textbook 2011 Springer-Verlag Berlin

reaching

The moduli space of stable curves,construct . as an analytic space, and then we show that this analytic space has a natural structure of algebraic space. After a utilitarian introduction to orbifolds and stacks, in particular to Deligne–Mumford stacks, we then show that . is just a coarse reflection of a more fundamental object, the

harpsichord

Line bundles on moduli,t. We introduce several natural bundles on moduli, including the Hodge bundle and the point bundles, and the stack divisors corresponding to the codimension one components of the boundary. We then discuss the theory of the determinant of the cohomology, which is well suited to producing line bundles

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折磨

迎合

Smooth Galois covers of moduli spaces,act, since varieties of this kind, even when singular, have a naturally defined intersection theory. We describe this quotient representation, starting from the case of smooth curves where the constructions are considerably more transparent from a geometrical point of view. Using the theory of admis

obstruct

FAR

Cellular decomposition of moduli spaces, which we review in Sections 5 and 6. The cells of the decomposition are labelled by ribbon graphs, and the decomposition itself is equivariant under the action of the Teichmüller modular group. We then extend this decomposition to the bordification of Teichmüller space introduced in Chapter XV. By