Author

Omkar Javadekar

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Preprint Sep 2026

The Betti numbers and Golodness of numerical semigroup rings of Sally type

We determine explicit formulae for the Betti numbers of the defining toric ideals of two families of numerical semigroups of Sally type, resolving and extending beyond several conjectures of Goel--\c{S}ahin--Singh--Srinivasan. Our approach uses Ap\'ery resolutions and their specialisations. For the family \[ \Gamma_m(n...

Manav Batavia, Omkar Javadekar, Manohar Kumar · 0 citations

Preprint Aug 2026

On the weak Lefschetz property of Artinian Gorenstein algebras of codimension three in arbitrary characteristic

Let $\mathsf k$ be a field, $S=\mathsf k[x,y,z]$, and $R=S/I$ be a standard graded Artinian Gorenstein $\mathsf k$-algebra of codimension three. The $h$-vector of such an algebra is known to be symmetric and unimodal. Mir\'o-Roig proved that if $\mathsf k$ is algebraically closed of characteristic zero and the $h$-vect...

Omkar Javadekar · 0 citations