8 problems

Work over an algebraically closed field of characteristic $0$. Let $C\subset\mathbb{P}^n$ be a linearly normal embedding of a smooth curve of genus $g$ by a line bundle $L$, and le…

Let $(A,L)$ be a polarized abelian variety of dimension $g$. A polarization is of type $(d_1,\ldots,d_g)$ when its elementary divisors are $d_1\mid\cdots\mid d_g$. Normal generatio…

Let $(A,L)$ be a polarized abelian variety of dimension $g$. A polarization is of type $(d_1,\ldots,d_g)$ when its elementary divisors are $d_1\mid\cdots\mid d_g$. Normal generatio…

Let $X$ be a projective variety, let $L$ define an embedding $X\subseteq\mathbb{P}^r$, and let $\Sigma_k(X,L)$ denote the $k$-th secant variety. Suppose that $L=L_1\otimes L_2$, wh…

Let $X$ be a projective toric variety of dimension $n$, let $T$ be its algebraic torus, and let $L$ be an ample line bundle on $X$. Let $p$ be a nonnegative integer, and let Proper…

Let $M$ be a lattice and let $M_{\mathbb{R}}=M\otimes_{\mathbb{Z}}\mathbb{R}$. For a lattice polytope $P\subseteq M_{\mathbb{R}}$, let $L(P)$ denote its lattice length, and write…

Fuentes García's conjecture. $L$ is projectively normal if

Let $X$ be a smooth Calabi-Yau threefold and $L$ a globally generated, ample line bundle. For a surface $S\in |L|$, write $|L\mathbin{\vert}_S|$ for the restriction of the linear s…