The Faltings Riemann-Roch Theorem
In this chapter we prove the Faltings Riemann-Roch theorem, assuming the existence of certain volumes on the cohomology of a line sheaf on a curve over the complex numbers. The next chapter will be devoted to proving the existence of these volumes by analytic means. Also we shall postpone to the next chapter another result of analysis needed as a lemma to justify one of Faltings’ applications of his theorem. Thus the present chapter constitutes a natural sequel in the style of algebraic geometry with metrized line sheaves, continuing the ideas of the adjunction formula.
KeywordsExact Sequence Line Sheaf Euler Characteristic Canonical Sheaf Generic Fiber
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