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math.AG2026

Components of simple and non--simple type of Hurwitz schemes

Ciro Ciliberto, Andreas Leopold Knutsen, Sara Torelli

Let , with , be the Hurwitz space, parametrizing all morphisms of degree , with points $x_1,\…

math.AG2026

On the Hurwitz existence problem for branched covers of the projective line

Ciro Ciliberto, Andreas Leopold Knutsen, Sara Torelli

We give an alternative proof of the Hurwitz existence problem for branched covers of in the case where the number of ramification points equals the number of branch…

math.AG2026

Brill-Noether loci of pencils with prescribed ramification on moduli of curves and on Severi varieties on surfaces

Andreas Leopold Knutsen, Sara Torelli

Under the assumption that the adjusted Brill-Noether number is at least , we prove that the Brill-Noether loci in of pointed curves carrying…

math.AG2024

Distinguishing Brill-Noether loci

Asher Auel, Richard Haburcak, Andreas Leopold Knutsen

We construct curves carrying certain special linear series and not others, showing many non-containments between Brill-Noether loci in the moduli space of curves. In particular, we…

math.AG2024

Rational curves and Seshadri constants on Enriques surfaces

Concettina Galati, Andreas Leopold Knutsen

We prove that classes of rational curves on very general Enriques surfaces are always -divisible. As a consequence, we prove that the Seshadri constant of any big and nef line b…