7 papers
The Betti numbers and Golodness of numerical semigroup rings of Sally type
Manav Batavia, Omkar Javadekar, Manohar Kumar
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 conj…
The arithmetic rank of nullcones of classical invariant rings
Manav Batavia, Aryaman Maithani, Kesavan Mohana Sundaram
We compute the arithmetic rank of nullcone ideals arising from natural actions of the special linear, orthogonal, and symplectic groups on direct sums of copies of their standard a…
Elimination Templates in Macaulay2
Manav Batavia, Cheng Chen, Anna Natalie Chlopecki +4
We introduce the package \texttt{EliminationTemplates} for the Macaulay2 computer algebra system, which provides tools for constructing automatic solvers for families of zero-dimen…
Vanishing of local cohomology in unramified mixed characteristic
Manav Batavia
Given an ideal in a regular local ring , the cohomological dimension of in is the index of the highest non-vanishing local cohomology of supported at . Determ…
The arithmetic rank of the residual intersections of a complete intersection ideal
Manav Batavia, Kesavan Mohana Sundaram, Vaibhav Pandey +1
The arithmetic rank of an ideal in a polynomial ring over an algebraically closed field is the smallest number of equations needed to define its vanishing locus set-theoretically.…
Syzygies of associated graded modules
H. Ananthnarayan, Manav Batavia, Omkar Javadekar
Given a finitely generated module over a Noetherian local ring , we give a characterization for the first syzygy of the associated graded module to be…
Fermat's polygonal number theorem for repeated generalized polygonal numbers
Soumyarup Banerjee, Manav Batavia, Ben Kane +5
In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain t…