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TateOnProducts :: cornerCohomologyTablesOfUa

cornerCohomologyTablesOfUa -- cohomology tables of Ua and related complexes - Example 3.6

Synopsis

Description

Given a degree list {a1,...,at}  with 0 ≤ai ≤ni for Ua = Λa1 U1 ⊗...⊗  Λat Ut part of the Tate resolution T=T(Ua) gets computed. Four cohomology tables and two betti tables get returned: The cohomology table

of T,

of the corner complex of T at c=-a,

of the Beilinson Window of T,

of the shifted corner complex at {1,..,1}, shifted by [-1],

and the two betti table with respect to total degree of the two corner complexes above.

This illustrates the validity of Example 3.6 of our paper Tate Resolutions on Products of Projective Spaces. Current implementation handles only the case of two factors.

i1 : netList cornerCohomologyTablesOfUa({1,2},{1,1})

     +-----------------------+
o1 = || 48h  24h 0 24  48   ||
     || 30h  15h 0 15  30   ||
     || 16h  8h  0 8   16   ||
     || 6h   3h  0 3   6    ||
     || 0    0   0 0   0    ||
     || 2h2  h2  0 h   2h   ||
     || 0    0   0 0   0    ||
     || 6h3  3h3 0 3h2 6h2  ||
     || 16h3 8h3 0 8h2 16h2 ||
     +-----------------------+
     || 0    24h 0 24 48 |   |
     || 0    15h 0 15 30 |   |
     || 0    8h  0 8  16 |   |
     || 0    3h  0 3  6  |   |
     || 0    0   0 0  0  |   |
     || 0    h2  0 h  2h |   |
     || 0    0   0 0  0  |   |
     || 6h4  0   0 0  0  |   |
     || 16h4 0   0 0  0  |   |
     +-----------------------+
     || 0 0  0 0 0 |         |
     || 0 0  0 0 0 |         |
     || 0 0  0 0 0 |         |
     || 0 0  0 0 0 |         |
     || 0 0  0 0 0 |         |
     || 0 h2 0 0 0 |         |
     || 0 0  0 0 0 |         |
     || 0 0  0 0 0 |         |
     || 0 0  0 0 0 |         |
     +-----------------------+
     || 0    0   0 24k 48k | |
     || 0    0   0 15k 30k | |
     || 0    0   0 8k  16k | |
     || 0    0   0 3k  6k  | |
     || 0    0   0 0   0   | |
     || 2h2  h2  0 0   0   | |
     || 0    0   0 0   0   | |
     || 6h3  3h3 0 0   0   | |
     || 16h3 8h3 0 0   0   | |
     +-----------------------+
     |       -2 -1 0 1  2    |
     |total: 13  4 1 6 25    |
     |    0:  3  . . .  .    |
     |    1: 10  4 . .  .    |
     |    2:  .  . 1 .  .    |
     |    3:  .  . . .  .    |
     |    4:  .  . . 6 25    |
     +-----------------------+
     |       -2 -1 0 1  2    |
     |total: 14  3 1 5 17    |
     |   -1: 14  3 . .  .    |
     |    0:  .  . . .  .    |
     |    1:  .  . . .  .    |
     |    2:  .  . 1 2  3    |
     |    3:  .  . . 3 14    |
     +-----------------------+

Ways to use cornerCohomologyTablesOfUa :