5 problems

Cohen–Macaulayness of Severi strata for miniversal deformations of $A_{2k}$
Let $A_{2k}$ be the indicated singularity, let $S$ be the base of its miniversal deformation, and let $D(\ell)\subset S$ denote the corresponding Severi stratum. For integers…
openFrom paperscohen-macaulay severi-varieties singularity-theory
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4
Bj\orner--Swartz conjecture on dual WLP for doubly Cohen--Macaulay complexes
Bjorner--Swartz conjecture. Every doubly Cohen--Macaulay simplicial complex has the dual WLP.
openFrom paperscohen-macaulay lefschetz-properties simplicial-complexes
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4
Stanley's partitionability conjecture for Cohen–Macaulay simplicial complexes
Stanley's partitionability conjecture. Every Cohen–Macaulay simplicial complex is partitionable.
solvedFrom paperscohen-macaulay partitionability simplicial-complexes
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4
Bj"orner–Swartz inequalities and M-sequence conjecture
Let $\Delta$ be a $(d-1)$ -dimensional simplicial complex that is doubly Cohen–Macaulay over $k$ . Write ${\mathfrak h}_i(\Delta)$ for its ${\mathfrak h}$ -vector and…
openFrom paperscohen-macaulay face-vectors simplicial-complexes
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3
The Björner–Swartz conjecture for g-vectors of doubly Cohen–Macaulay complexes
Björner–Swartz conjecture. The $g$ -vector of any doubly Cohen–Macaulay complex is an $M$ -sequence.
openFrom paperscohen-macaulay f-vectors simplicial-complexes
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4

Cohen–Macaulayness of Severi strata for miniversal deformations of A2kA_{2k}A2k​