From the 1 of 6 linked papers with an AI index.
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Quasipolynomial behavior via constructibility in multigraded algebra
Hailong Dao, Ezra Miller, Jonathan Montaño +2
Piecewise quasipolynomial growth of Presburger counting functions combines with tame persistent homology module theory to conclude piecewise quasipolynomial behavior of constructib…
Periodicity of ideals of minors in free resolutions
Michael K. Brown, Hailong Dao, Prashanth Sridhar
We study the asymptotic behavior of the ideals of minors in minimal free resolutions over local rings. In particular, we prove that such ideals are eventually 2-periodic over compl…
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…
Regularity, singularities and -vector of graded algebras
Hailong Dao, Linquan Ma, Matteo Varbaro
Let be a standard graded algebra over a field. We investigate how the singularities of affect its -vector, which is the coefficients of the numerator of its Hilbert seri…
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…