Soham Ghosh

collaborators

4 papers

math.AC2026

Proof of the Casas-Alvero conjecture

Soham Ghosh

The Casas-Alvero conjecture states that if $f (X)$ is a monic univariate polynomial of degree $d$ over a characteristic $0$ field $K$ such that $g cd (f, f_{i})$ is non-triv…

math.AG2026

KovÃ¡cs' conjecture on characterization of projective space and hyperquadrics

Soham Ghosh

We prove KovÃ¡cs' conjecture that claims that if the $p^{t h}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{t h}$ exterior power of an…

math.AG2025

Tropical PoincarÃ© bundle, Fourier-Mukai transform, and a generalized PoincarÃ© formula

Soham Ghosh, Farbod Shokrieh

We construct a tropical analogue of the PoincarÃ© bundle and prove a (cohomological) Fourier-Mukai transform for real tori with integral structures. We then prove a tropical analog…

math.AG2025

A finiteness result towards the Casas-Alvero Conjecture

Soham Ghosh

The Casas-Alvero conjecture predicts that every univariate polynomial over an algebraically closed field of characteristic zero sharing a common factor with each of its Hasse-Schmi…