Author

Desiree Martin

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Preprint Sep 2026

DG Algebra Structures on Mapping Cones with an Application to Edge Ideals

We generalize a construction of Herzog and Takayama pertaining to differential graded algebra structures on mapping cones. Via this generalization, we provide the minimal free resolution of the edge ideal of a new graph built from suspension over a vertex cover of an old graph, and we discuss when this process preserve...

Hugh Geller, Desiree Martin, Matthew Mastroeni et al. · 0 citations

Preprint Aug 2026

Relating the Exterior Algebra of the Conormal Module to the Tor Algebra

For any ideal $I$ (whose projective dimension need not be finite) in a local Noetherian ring $R$, we show that, if the conormal module $I/I^2$ has a free summand given by $F$, the natural map from $\bigwedge F$ to $\text{Tor}_{*}^{R}(R/I,R/I)$ splits as algebras. To achieve this, we use dg algebra techniques and remode...

Desiree Martin · 0 citations