Index
k-very ampleness, 78
Betti
numbers (graded), 4
table, 5, 58
Brill-Noether
divisor, 112, 115
locus, 53
number, 54
Brill-Noether-Petri generic curve, 54, 55,
77, 82, 88
Castelnuovo lemma, 41
Cayley-Bacharach property, 75
Clifford
dimension, 57, 76
index, 49, 56–58, 77
conjecture
Eisenbud-Lange-Martens-Schreyer –, 56
Green, 103
Green –, 58, 60, 79, 88, 97, 99, 100, 109,
116
generalized –, 61
specific –, 93
Green-Lazarsfeld –, 59, 98–100
Harris-Morrison –, 112, 115
Eagon-Northcott complex, 69
gonality, 55, 59
Hodge structure
infinitesimal variation of –, 106
variation of –, 106
kernel bundle, 13
Koszul
class, 29, 30, 32
and rank-2 bundles, 43, 48
rank of –, 29, 37
scrollar –, 38, 95
cohomology, 2, 5, 7
and Hodge theory, 110
evaluation map on –, 15, 16
nonvanishing of –, 45, 48, 57, 59
projection map on –, 15–17, 60, 71
restriction of –, 19
semicontinuity of –, 9, 10, 60
vanishing of –, 25, 27
complex, 1, 2, 6, 7, 87
Lazarsfeld-Mukai bundle, 76, 77, 79, 88, 89,
92
minimal resolution, 4, 58
property
(Mk), 59
(Np), 58, 60, 61, 113
regularity
Castelnuovo–Mumford, 24, 25
slope
of a fibered surface, 115
of a moduli divisor, 112
of the moduli space, 112
syzygy, 4
ideal, 30
scheme, 30, 34
generic –, 32–34
theorem
Kp,1 –, 41
Clifford –, 54, 56
duality for Koszul cohomology, 21, 58,
60
explicit Noether-Lefschetz –, 107
Hilbert syzygy –, 5
Lefschetz for Koszul cohomology, 20
Voisin
description of Koszul cohomology, 68
proof of the Green generic conjecture, 79,
88
125
Previous Page Next Page