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math.AC2022★ 1 cited
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…
math.AC2022★ 1 cited
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…
math.AC2022
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,…