arXiv subjects

Aniketh Sivakumar

Publications and source records attributed to Aniketh Sivakumar.

3 recordsLinked to original sources

arXiv2026

Polynomial interpolation and the Waldschmidt constant of points in projective space

We establish Chudnovsky's Conjecture and, more generally, Demailly's Conjecture for any finite set of points in $\mathbb{P}^n_k$, where $k$ is an algebraically closed field of characteristic 0. The key idea of passing to positive characteristic, as well as the broad plan of the proof, was suggested by ChatGPT-5.6 Sol. All mathematical arguments and proofs in this paper were developed, written, and verified by the authors.

math.AG↗

arXiv2026

The multiplicity sequence of monomial ideals

We give a convex-geometric formula for the multiplicity sequence of a monomial ideal in terms of mixed volumes of polytopes constructed from its Newton polyhedron. We also construct a counterexample to a conjecture of Achilles and Manaresi proposing a different volume formula for the multiplicity sequence. Finally, we derive a mixed-volume formula for the mixed multiplicities of arbitrary monomial ideals.

math.AC↗

arXiv2024

Partial Betti splittings with applications to binomial edge ideals

We introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, H\`a, and Van Tuyl. Given a homogeneous ideal $I$ and two ideals $J$ and $K$ such that $I = J+K$, a partial Betti splitting of $I$ relates some of the graded Betti of $I$ with those of $J, K$, and $J\cap K$. As an application, we focus on the partial Betti splittings of binomial edge ideals. Using this new technique, we generalize results of Saeedi Madani and Kiani related to binomial edge ideals with cut edges, we describe a partial Betti splitting for all binomial edge ideals, and we compute the total second Betti number of binomial edge ideals of trees.

math.AC↗