Examples of infinitely many $(-1)$-curves with higher genus on elliptic surfaces

Abstract

In this article, for every integer $g>1$, we construct the first example of an elliptic surface with infinitely many smooth $(-1)$-curves of genus $g$, settling an open question of Bauer et al. [Duke Math. J. 162 (10) (2013), 1877-1894].

7 pages, comments are welcome!