5 papers
Infinitely many Lefschetz pencils on ruled surfaces
Seraphina Eun Bi Lee, Carlos A. Serván
We show that any ruled surface with admits infinitely many inequivalent Lefschetz pencils of fixed genus and number of base points. Our proof proceeds by building in…
Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves
Carlos A. Serván
We show that totally geodesic subvarieties of the moduli space of genus curves with marked points, endowed with the Weil--Petersson metric, are locally r…
Lefschetz fibrations with infinitely many sections
Seraphina Eun Bi Lee, Carlos A. Serván
The Arakelov--Parshin rigidity theorem implies that a holomorphic Lefschetz fibration of genus admits only finitely many holomorphic sections $σ:S^2 \to M…
Isometric embeddings of Teichmüller spaces are covering constructions
Frederik Benirschke, Carlos A. Serván
Pulling back complex structures along a branched covering induces a holomorphic isometric embedding of Teichmüller spaces. We show that for dimension at least , all isometric em…
On the uniqueness of the Prym map
Carlos A. Serván
The classical Prym construction associates to a smooth, genus complex curve equipped with a nonzero cohomology class , a principally pol…