10 JOSEP ALVAREZ MONTANER AND SANTIAGO ZARZUELA

• Linear maps: We have the following commutative diagram:

where

Vi

is induced by the inclusion

Ta

:;;;

Ta+E,.

REMARK

5.3. By using the previous result and Theorem 4.2 we recover the

result on the module structure of the local cohomology modules

HJ(R)

given by

M. Mustata

[10].

Namely, if (- )* denotes the dual of a C-vector space, the graded

pieces of

HJ(R)

are:

[H[(R)]-cx

~

(Hr-2(Ta;

C))*~

jjr-

2(Ta;

C), a

E

{0,

l}n,

and the multiplication map

Xi:

[H[(R)]-a-E,

-----

[H[(R)]-cx

is determined by the

following commutative diagram:

where

Vi

is induced by the inclusion

Ta

:;;;

Ta+E;.

References

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J.

Pure Appl. Algebra, 150 (2000), 1-25.

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[4]

J.-

E. Bjork, Analytic V-modules and applications, Mathematics and its Applications, Vol.

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J.

Math., 1-2

(1978), 237-261.

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J.

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J.

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