HODGE THEORY AND LOCAL TORELLI

collapsing map, 29

dual vector space, 30

genus, 31

third tensor power of a line bundle, 35

intersection, 39

complete linear system, 39

topological Euler characteristic, 40

canonical divisor, 41

moduli space of smooth curves, 42

moduli space of stable curves, 42

smooth subscheme of stable 5-canonical curves,

projective general linear group, 43

determinant of Hodge bundle, 43

line bundle corresponding to the divisor A, 4

group of line bundles on X, 44

first Chern class of L , 44

A

first Chern class of L. , 44

universal quotient bundle over a Grassmannian,

universal subbundle over a Grassmannian, 48

Schubert cycle, 50