We calculate the minimal attached primes of the local cohomology modules of the binomial edge ideals of block graphs. In particular, we obtain a combinatorial characterisation of which of these modules are non-vanishing. We further conjecture that every attached prime of these modules is minimal, and, more strongly, that the binomial edge ideals of block graphs are sequentially Cohen-Macaulay.
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David Williams (2024) studied this question.
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