Carlos A. Serv'an

activity

20242026

collaborators

3 papers

math.GT2026

Infinitely many Lefschetz pencils on ruled surfaces

Seraphina Eun Bi Lee, Carlos A. Serván

We show that any ruled surface $X$ with $χ (X) < 0$ admits infinitely many inequivalent Lefschetz pencils of fixed genus and number of base points. Our proof proceeds by building in…

math.GT2025

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 $M_{g, n}$ of genus $g$ curves with $n$ marked points, endowed with the Weil--Petersson metric, are locally r…

math.GT2024

Lefschetz fibrations with infinitely many sections

Seraphina Eun Bi Lee, Carlos A. Serván

The Arakelov--Parshin rigidity theorem implies that a holomorphic Lefschetz fibration $π : M \to S^{2}$ of genus $g \geq 2$ admits only finitely many holomorphic sections $σ:S^2 \to M…