Rafael Mendes de Oliveira, Akash Sengupta

Let $\mathcal{F} = \{F_1, \ldots, F_m\}$ be a finite set of irreducible homogeneous multivariate polynomials of degree at most $3$ such that $F_i$ does not divide $F_j$ for $i\neq j$.

We say that $\mathcal{F}$ is a cubic radical Sylvester-Gallai configuration if for any two distinct $F_i,F_j$ there exists a ...
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Abhibhav Garg, Rafael Mendes de Oliveira, Shir Peleg, Akash Sengupta

We prove a higher codimensional radical Sylvester-Gallai type theorem for quadratic polynomials, simultaneously generalizing [Han65, Shp20]. Hansen's theorem is a high-dimensional version of the classical Sylvester-Gallai theorem in which the incidence condition is given by high-dimensional flats instead of lines. We generalize Hansen's theorem to the setting of quadratic forms ... more >>>