Opened 7 years ago

# Can have a module have two different Hilbert series ??

Reported by: Owned by: wbruns@… hannes major 4-2-0 and higher singular-kernel 4-0-3 Hilbert series, minbase conca@…

### Description

The computation below is part of an ongoing project with Aldo Conca.

We want to test the question whether the module K3 is Cohen-Macauly and self-dual. We use the fact that K3 is a module over K0 which is a Gorenstein ring, namely the coordinate ring of the Grassmannian G(5,2) of dim 3 vector spaces in the 5-dimensional vector space.

4 t0 92 t1 4 t2 dimension (proj.) = 6 degree (proj.) = 100

Comment: At this point we are happy since the result coincides with an independent computation of the Hilbert series. Moreover, the h-vector (4,92,4) fulfills 2 necessary conditions: (i) it has nonnegative enties, (ii) it is palindromic. Now we want to test our conjecture.

module K3D=Hom(K3,K0); dimension of Hom: 7

K3D=std(K3D); hilb(K3D); 2 t0 62 t1 -980 t2 6190 t3 -23140 t4 58214 t5 -104676 t6 138710 t7 -137280 t8 101530 t9 -55484 t10 21866 t11 -5980 t12 1090 t13 -140 t14 18 t15 -2 t16

2 t0 88 t1 8 t2 2 t3 dimension (proj.) = 6 degree (proj.) = 100

Comment: Our conjecture is dstroyed ... K3D has adifferent h-vector ... But now a miracle happens...

K3D=minbase(K3D); K3D=std(K3D); hilb(K3D); 4 t0 40 t1 -880 t2 5980 t3 -23140 t4 59488 t5 -108680 t6 145860 t7 -145860 t8 108680 t9 -59488 t10 23140 t11 -5980 t12 880 t13 -40 t14 -4 t15

4 t0 92 t1 4 t2 dimension (proj.) = 6 degree (proj.) = 100

Comment: Whow !!!!!!!!!! It has the right h-vecor -- or not? Conjecture rescued. How can minbase change the h-vector ??????????????

quit;

### comment:1 Changed 6 years ago by hannes

Owner: changed from somebody to hannes
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