60 citations · 291 across the 64 of their papers we have counts for
59 papers · 1 filter
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…
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…
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 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…
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…
Counting geometric branches via the Frobenius map and -nilpotent singularities
Hailong Dao, Kyle Maddox, Vaibhav Pandey
We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the p…
Elias Ideals
Hailong Dao
Let be a one dimensional local Cohen-Macaulay ring. An -primary ideal of is Elias if the types of and of are equal. Canonical and…
Ulrich split rings
Hailong Dao, Souvik Dey, Monalisa Dutta
A local Cohen--Macaulay ring is called Ulrich-split if any short exact sequence of Ulrich modules split. In this paper we initiate the study of Ulrich split rings. We prove several…
Burch index, summands of syzygies and linearity in resolutions
Hailong Dao, David Eisenbud
The Burch index is a new invariant of a local ring whose positivity implies a kind of linearity in resolutions of -modules. For example, if has depth zero and Burch inde…
Linearity of Free Resolutions of Monomial Ideals
Hailong Dao, David Eisenbud
We study monomial ideals with linear presentation or partially linear resolution. We give combinatorial characterizations of linear presentation for square-free ideals of degree 3,…
On the Lefschetz Property for quotients by monomial ideals containing squares of variables
Hailong Dao, Ritika Nair
Let be an (abstract) simplicial complex on vertices. One can define the Artinian monomial algebra $A(Δ) = \Bbbk[x_1, \ldots, x_n]/ \langle x_1^2, \ldots, x_n^2, I_Δ \rangle…
Stable trace ideals and applications
Hailong Dao, Haydee Lindo
We study stable trace ideals in one dimensional local Cohen-Macaulay rings and give numerous applications.
Reflexive modules, self-dual modules and Arf rings
Hailong Dao
We prove a tight connection between reflexive modules over a one-dimensional ring and its birational extensions that are self-dual as -modules. Consequently, we show that a…
On reflexive and -Ulrich modules over curve singularities
Hailong Dao, Sarasij Maitra, Prashanth Sridhar
We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits the concept of -Ulrich modules.
On colon operations and special types of ideals
Hailong Dao
We record a general asymptotic formula for colon of ideals and proceed to give some applications regarding -full, weakly -full, and full ideals.
Trace of canonical modules, annihilator of Ext, and classes of rings close to being Gorenstein
Hailong Dao, Toshinori Kobayashi, Ryo Takahashi
In this note we study trace ideals of canonical modules. Characterizations of the trace ideals in terms of annihilators of certain Ext modules are given. We apply our results to st…
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…
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…
On asymptotic vanishing behavior of local cohomology
Hailong Dao, Jonathan Montaño
Let be a standard graded algebra over a field , with irrelevant maximal ideal $\fm$, and a homogeneous -ideal. We study the asymptotic vanishing behavior of the grade…
Cohomologically full rings
Hailong Dao, Alessandro De Stefani, Linquan Ma
Inspired by a question raised by Eisenbud-Mustaţă-Stillman regarding the injectivity of maps from modules to local cohomology modules and the work by the third author w…
Hom and Ext, Revisited
Hailong Dao, Mohammad Eghbali, Justin Lyle
Let be a commutative Noetherian local ring and be finitely generated -modules. We prove a number of results of the form: if $\mbox{Hom}_R(M,N)$ has some nice propertie…
Symbolic powers of ideals
Hailong Dao, Alessandro De Stefani, Eloísa Grifo +2
We survey classical and recent results on symbolic powers of ideals. We focus on properties and problems of symbolic powers over regular rings, on the comparison of symbolic and re…