dimk dimension of a k-vector space 49
Γ∗F graded module associated to a sheaf 49
Γ(X, F ) module of global sections 50
χ(F ) Euler characteristic of F 50
Supp(F ) support of a sheaf F 50
PF Hilbert polynomial of F 50
pa(X) arithmetic genus of X 51
sheaf of p-forms on a scheme X/A 52
R(X) field of rational functions on
an integral scheme X/A 52
integral for a projective variety X 55, 101
δF duality isomorphism 55, 94, 102
R, M completion of a local ring R or an R-module M 56
Resx residue at a closed point x 56, 95
X(k) set of k-rational points of X 57
V+(I) zero-set of a homogeneous ideal I in Proj S 58
affine space over k 58
G(f) = Gf degree form of a polynomial f 58
TP (V ) tangent space of a variety V at P 61
grad f gradient of a polynomial f 63
, standard scalar product 63
H∞ hyperplane at infinity 63
fXi =
partial derivative of f with respect to Xi 63
tr(ϕ) trace of an endomorphism 65
trS/R trace map of an algebra 65
ωS/R canonical (dualizing) module 65, 84
Q(R) full ring of quotients of a ring R 66
CS/R Dedekind complementary module 66
dD(S/R) Dedekind different 66
fT/S conductor of an algebra T/S 67
k(SP) residue field of SP 68
µ(M) minimal number of generators of M 68
µP(M) minimal number of generators of MP 68
rP Cohen-Macaulay type at P 68
Max S set of maximal ideals of S 69
δ canonical multiplication map S ⊗R S S 70
dN (S/R) Noether different 70
dK (S/R) ahler different 70
ezoutian 72
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