60 citations · 291 across the 64 of their papers we have counts for
5 papers · 1 filter
Symbolic analytic spread: upper bounds and applications
Hailong Dao, Jonathan Montaño
The symbolic analytic spread of an ideal is defined in terms of the rate of growth of the minimal number of generators of its symbolic powers. In this article we find upper bou…
Burch ideals and Burch rings
Hailong Dao, Toshinori Kobayashi, Ryo Takahashi
We introduce the notion of Burch ideals and Burch rings. They are easy to define, and can be viewed as generalization of many well-known concepts, for example integrally closed ide…
Minimal Cohen-Macaulay Simplicial Complexes
Hailong Dao, Joseph Doolittle, Justin Lyle
We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give suff…
On monomial Golod ideals
Hailong Dao, Alessandro De Stefani
We study ideal-theoretic conditions for a monomial ideal to be Golod. For ideals in a polynomial ring in three variables, our criteria give a complete characterization. Over such r…
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…