# Research

### Publications:

A. Carney, R. Hortsch, M. Zieve. *Polynomial mappings of the
rationals are at most six to one off a finite set.* In preparation.

R. Hortsch. * Counting elliptic curves of bounded Faltings height*. Accepted to Acta Arithmetica. Arxiv link.

M. J. Bertin, A. Garbagnati, R. Hortsch, O. Lechacheux, M Mase, C.
Salgado, U. Whitcher. * Classifications of Elliptic Fibrations of a
Singular K3 Surface.* Women in Numbers Europe: Research
Directions in Number Theory. Arxiv link to paper.

R. Hortsch. *On the canonical representation of curves in
positive characteristic.* New York J. Math. 18 (2012) 911-924. Article.

R. Hortsch, I. Kriz, and A. Pultr. *A universal approach to
vertex algebras.* Journal of Algebra 324 (2010), 1731-1753. Article.