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For questions related to divisors in the sense of algebraic geometry (Cartier divisors, Weil divisors and so on). For question on divisors in the number theoretic sense please use the tag divisors-multiples.

2 votes
1 answer
235 views

Intersection of translate of divisors on abelian variety

Does there exist an irreducible divisor $D$ on $A$ such that the collection of divisors $\{ D + x_i\}_{1\leq i \leq m^{2n}}$ are in general position i.e., for any $I \subset \{ 1,\dots,m^{2n}\}$, $\dim …
2 votes
0 answers
66 views

Irreducible components over a singular divisor

Setup. Let $K$ be an algebraically closed field of characteistic zero, let $X/K$ be a smooth projective surface and let $Z \subset X$ be an integral curve which is nonsingular except for a finite set …