8

JOSEP ALVAREZ MONTANER AND SANTIAGO

ZARZUELA

Applying [1, 3.8] there is a local cohomology module

different from zero and its

characteristic cycle is

CC(H2(R))

=

T* X+ T* X+ T* X+ 2 T* X.

I x(1,1,o)

x(l,o,l) xo,l,lJ x(l,l,lJ

In particular, we only have to study the vertices of then-hypercube

(1iJ(R))o:

for

a=

(1,1,0),(1,0,1),(0,1,1),(1,1,1).

We have the Cech complex:

R

[x11 xJ

R

[x1:2xJ

EB EB

• do [

1 ]

Cj:

o-R-R X1X3

~

R

[x1:2X3]

EB EB

R

[x21 xJ

R

[x1:2xJ

• The complex *HomR(Cj,E(l,l,l)) is of the form:

do d1

d2

0----0----0---- C3

----

C ---- 0

whe" d,

~

(-

D .

Then,

we

get the vete"

(HJ(R))(l,l,l)

=

H2(*HomR(Cj, E(l,l,l)))

=

C2

.

• The complexes *HomR(Cj, Eo:), for a=

(1, 1, 0), (1, 0, 1), (0,

1, 1),

are of the

form:

do d1 d2

0----0---- C ---- C3

----

C ----0

whe;e d,

~

(I 0 -I) and

d,

~

(-

D .

Then, we get the vert ice"

(1iJ(R)

)o:

=

H 2(*HomR(Cj, Eo:))

=

C, for a=

(1, 1, 0), (1, 0, 1), (0, 1, 1).

Computing the

linear maps among these vertices in an adequate basis we get

then-hypercube:

0

/!~

0 0 0

!XX!

c c c

~lJ,~

c