15 problems

Let $X$ be a variety, let $\mathcal{L}$ be a line bundle on $X$, and let $\mathbb{X}\subseteq X$ be a zero-dimensional scheme. The scheme $\mathbb{X}$ imposes independent condition…

For interpolation problems on the plane, let a linear system of plane curves have prescribed singularities at specified points. Segre's conjecture. The superabundance of such a lin…

Let $(X_0,X_1)$ be a Banach couple, and call a Banach space an interpolation space for the couple when it is an intermediate space associated with $(X_0,X_1)$ in the sense of inter…

Let $d\in\mathbb{N}$, let $p$ and $\gamma$ be parameters for which the weighted Sobolev spaces below are defined, let $X$ be the underlying Banach space, and let…

For $n\ge 3$, let $\mathbb{T}(n,d;x)'$ denote the set of minimally Terracini sets of $x$ points in $\mathbb{P}^n$ with respect to $\mathcal{O}_{\mathbb{P}^n}(d)$: these are sets…

Let ${\mathbb{T}}(n,d;x)'$ denote the locus of minimally Terracini sets of $x$ points in ${\mathbb{P}}^n$ with respect to ${\mathcal{O}}_{{\mathbb{P}}^n}(d)$, where minimality mean…

Interpolation embedding conjecture. Such an interpolation result should hold for the case of a weak Lipschitz domain.

Let $X$ be a reflexive Banach space, and let $\overline X^*$ denote its conjugate dual. Suppose that $X\cap\overline X^*$ is dense in both $X$ and $\overline X^*$, and that the int…

Let $(X,X^*)$ be an interpolation pair of Banach spaces with a common unconditional basis, with a continuous inclusion $X^*\to X$, and suppose that $(X^*,X)_{1/2}=\ell_2$ with diff…

Let $R={\mathbb C}[x,y,z]$, let $Y=\{P_1,\ldots,P_r\}$ be a general set of points in $\mathbb{P}^2$, and let $I_Y$ be its defining ideal. An irreducible homogeneous polynomial…

The paper considers normed interpolation spaces between $\ell^{1}$ and $\ell^{q}$, and Theorem 4.1 establishes the relevant characterization for positive exponents in the normed se…

Let ${}_{\Sigma}L_p$ denote the family of spaces associated with the surface $\Sigma$, and let $[\,\ ]_{\theta}$ and $(\,\ )_{\theta,r}$ denote the complex and real interpolation m…

Let $S=\{P_i:1\le i\le d\}$ be a set of $d$ generic points in $\mathbf{P}^n$ over a field $\mathbb{F}$ of characteristic zero. A cone polynomial is a homogeneous polynomial of degr…

Peetre's isometry conjecture. The coincidence of $\left\langle A_0,A_1\right\rangle_\theta$ and $\left[A_0,A_1\right]_\theta$ for couples of lattices is an isometry when…

Let $(S,L)$ be a polarized regular surface, let $p\in S$ be general, and suppose that $(S,L)$ is triple-point defective, meaning … Assume moreover that the map $\beta$ associated w…