高维Clifford-Severi等式
Higher dimensional Clifford-Severi equalities
AI总结：
本文刻画了高维Clifford-Severi不等式取等号时的簇与线丛条件，给出了等式成立的完整分类。
摘要：
设$X$为光滑复射影簇，$a\colon X\rightarrow A$为到阿贝尔簇的态射，使得$\mathrm{Pic}^0(A)$注入$\mathrm{Pic}^0(X)$，并设$L$为$X$上的线丛；记$h^0_a(X,L)$为$h^0(X,L\otimes a^*α)$在$α\in \mathrm{Pic}^0(A)$中的最小值。所谓的Clifford-Severi不等式已在arXiv:1303.3045 [math.AG]和arXiv:1606.03290 [math.AG]中得到证明；特别地，对任意$L$，体积有下界：$$\mathrm{vol}(L)\ge n! h^0_a(X,L),$$且若$K_X-L$为伪有效，则$$\mathrm{vol}(L)\ge 2n! h^0_a(X,L).$$本文刻画了上述Clifford-Severi不等式取等号的簇和线丛。
英文摘要：
Let $X$ be a smooth complex projective variety, $a\colon X\rightarrow A$ a morphism to an abelian variety such that $\mathrm{Pic}^0(A)$ injects into $\mathrm{Pic}^0(X)$ and let $L$ be a line bundle on $X$; denote by $h^0_a(X,L)$ the minimum of $h^0(X,L\otimes a^*α)$ for $α\in \mathrm{Pic}^0(A)$. The so-called Clifford-Severi inequalities have been proven in arXiv:1303.3045 [math.AG] and arXiv:1606.03290 [math.AG]}; in particular, for any $L$ there is a lower bound for the volume given by: $$\mathrm{vol}(L)\ge n! h^0_a(X,L),$$ and, if $K_X-L$ is pseudoeffective, $$\mathrm{vol}(L)\ge 2n! h^0_a(X,L).$$ In this paper we characterize varieties and line bundles for which the above Clifford-Severi inequalities are equalities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
