4 problems

Let $A$ be the most generic quadratic Artin–Schelter regular algebra of dimension four with four generators and six relations, and let its line scheme be the parameter space of lin…

Let ${\mathcal A}(\alpha)$ be the quadratic quantum algebra under consideration, let ${\mathfrak L}(\alpha)\subseteq {\mathcal V}(P)\subseteq {\mathbb P}^5$ be its line scheme, and…

Line-scheme conjecture. The line scheme of the most generic quadratic regular algebra of global dimension four should be isomorphic to the union of two spatial elliptic curves and…

Line-scheme conjecture. The line scheme of the most generic quadratic quantum ${\mathbb P}^3$ is isomorphic to the union of two spatial (irreducible and nonsingular) elliptic curve…