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math.AC2024
Betti numbers and linear covers of points
Hailong Dao, Ben Lund, Sreehari Suresh-Babu
We prove that for a finite set of points in the projective -space over any field, the Betti number of the coordinate ring of is non-zero if and only if l…
math.AC2024
Syzygies of the residue field over Golod rings
Doan Trung Cuong, Hailong Dao, David Eisenbud +3
Let be a Golod ring. We show a recurrent formula for high syzygies of interms of previous ones. In the case of embedding dimension at most , we provided complete d…
math.AC2024
Regularity of linearly presented squarefree monomial ideals
Hailong Dao, Thanh Vu
We prove a sharp bound for the regularity of a squarefree monomial ideal with a linear presentation. This result also answers in positive a question on the cohomological dimension…