6 problems

The resultant formula. If $V_1(A)=\emptyset$ and $V_2(A)\ne\emptyset$, then, up to a nonzero constant,

Let $R$ be the relevant bihomogeneous coordinate ring, let $U\subseteq R_{a,b}$ be basepoint free with $b\geq n+1$, and let $I_U$ have a syzygy $C$ in bidegree $(0,n)$ but no syzyg…

Let $\mathcal{C}$ be a planar algebraic curve of constant width whose support function is a trigonometric polynomial of degree $3$. Apart from the circle, whose defining polynomial…

Let $u_0(\underline{T}),u_1(\underline{T}),u_2(\underline{T})\in\mathbb K[\underline{T}]$ be homogeneous polynomials of degree $d$, without common factors, defining a birational pa…

Let $u>1$, and let ${\mathcal C}_{u,d}$ be the monomial plane curve parametrized by the monomials $T_0^d$, $T_0^{d-u}T_1^u$, and $T_1^d$. Let $\Phi_0$ be the presentation map defin…

Let $\Gamma(\overline{\mathcal{E}})$ be the hypersurface associated with the canal-surface construction, and let $w$ be the polynomial defined by formula. Write…