5,050 research outputs found
The arithmetical rank of the edge ideals of graphs with pairwise disjoint cycles
We prove that, for the edge ideal of a graph whose cycles are pairwise
vertex-disjoint, the arithmetical rank is bounded above by the sum of the
number of cycles and the maximum height of its associated primes
Cohomological dimension and arithmetical rank of some determinantal ideals
Let be a non-generic matrix of linear forms in a
polynomial ring. For large classes of such matrices, we compute the
cohomological dimension (cd) and the arithmetical rank (ara) of the ideal
generated by the -minors of . Over an algebraically closed
field, any -matrix of linear forms can be written in the
Kronecker-Weierstrass normal form, as a concatenation of scroll, Jordan and
nilpotent blocks. B\u{a}descu and Valla computed when
is a concatenation of scroll blocks. In this case we compute
and extend these results to concatenations of Jordan
blocks. Eventually we compute and
in an interesting mixed case, when contains both Jordan and scroll blocks.
In all cases we show that is less than the arithmetical
rank of the determinantal ideal of a generic matrix
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