Let X be a smooth variety and let L be an ample line bundle on X. If πalg 1 (X) is large, we show that the Seshadri constant ϵ(p∗L) can be made arbitrarily large by passing to a finite étale cover p : X' → X. This result answers affirmatively to a conjecture of J.-M. Hwang. Moreover, we prove an analogous result when π1(X) is large and residually finite. Finally, under the same topological assumptions, we appropriately generalize these results to the case of big and nef line bundles. More precisely, given a big and nef line bundle L on X and a positive number N > 0, we show that there exists a finite étale cover p : X' → X such that the Seshadri constant ϵ(p∗L; x) ≥ N for any x ϵ p-1B+(L) = B+(p∗L), where B+(L) is the augmented base locus of L.
|Original language||English (US)|
|Number of pages||10|
|Journal||Annali della Scuola Normale Superiore di Pisa - Classe di Scienze|
|State||Published - Jan 1 2019|
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Mathematics (miscellaneous)