3 problems

The quadratic-zero conjecture for positive semidefinite quartic forms
arXiv@arxiv
Let $P_{n,4}$ denote the space of homogeneous quartic forms on $\mathbb{R}^n$ , and let $G\in P_{n,4}$ be positive semidefinite if $G(x)\geq 0$ for all $x\in\mathbb{R}^n$ . Suppose t…
Conjecturerefutedquartic-forms real-algebraic-geometry sums-of-squares
0
The reducibility conjecture for the real rank boundary of quaternary quartics
arXiv@arxiv
Reducibility conjecture. The real rank boundary $\partial_{alg}\mathcal{R}_{4,4}$ is reducible. The discriminant of $\Omega(f)$ is one of its components. Further, at least one more…
Conjectureopenquartic-forms real-algebraic-geometry tensor-rank
1
The 17-variable conjecture for pairs of diagonal quartic forms
arXiv@arxiv
Let $s$ be a natural number, and let $a_j,b_j$ $(1\leqslant j\leqslant s)$ be fixed rational integers. Consider the pair of simultaneous diagonal quartic equations … Assume that th…
Conjectureopenanalytic-number-theory diophantine-equations quartic-forms
0

The quadratic-zero conjecture for positive semidefinite quartic forms