60 LORING TU Index Abelian surface, v Adjunction formula, 9 Ample cone on the moduli space of Ample divisor in the moduli space Betti number, 6 Birational local Torelli, 46 Biregular local Torelli, 46 Blowing up, 33,46 Bochner's theorem on the Euler characteristic of a weakly ample K&hler manifold, 53 Bogomolov-Miyaoka-Yau inequality, 50 Canonical extension of a Hodge bundle, 11,12 Cech coboundary operator, 24 Chern numbers, 48,52 of a weakly ample KShler manifold, 53 Classifying space for Hodge structures, 4 Clemens-Schmid exact sequence, 28,31,32,39 Coboundary operator, 24 Coherence theorem, 6 Cohomology bundle, 5 Collapsing map, 29 Compactified moduli space, 42 Cotangent map, 48,53,54 Curve with normal crossings, 26 mixed Hodge structure of, 26 Defined over 0, 21 Deformation retract, 29 Degeneration numerical invariants of, 21 Differentiable fiber bundle, 1 Differentials along the fiber, 6 Direct image sheaf, 6 Divisor of stable singular curves, 43 reduced, 8 with normal crossings, 7 Dolbeault cohomology, iv Double complex, 24 Dual graph, 23,31 Duality for a local complete intersection, 9 Poincare* duality, 29 Dualizing sheaf, 9 of a divisor, 9 curves, 42 of curves, 45
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