arXiv:2401.03821 [math.AG]AbstractReferencesReviewsResources
On the degree of irrationality of low genus $K3$ surfaces
Federico Moretti, Andrés Rojas
Published 2024-01-08Version 1
Given a general polarized $K3$ surface $S\subset \mathbb P^g$ of genus $g\le 14$, we study projections $S\hookrightarrow \mathbb P^g\dashrightarrow \mathbb P^2$ of minimal degree and their variational structure. In particular, we prove that the degree of irrationality of all such surfaces is at most $4$, and that for $g=7,8,9,11$ there are no rational maps $S\dashrightarrow \mathbb P^2$ of degree $3$ induced by the primitive linear system. Our methods combine vector bundle techniques \`a la Lazarsfeld with derived category tools, and also make use of the rich theory of singular curves on $K3$ surfaces.
Comments: 30 pages, 1 figure. Comments welcome!
Categories: math.AG
Related articles: Most relevant | Search more
The gonality theorem of Noether for hypersurfaces
arXiv:1609.02091 [math.AG] (Published 2016-09-07)
A note on Brill--Noether existence for graphs of low genus
arXiv:1603.05543 [math.AG] (Published 2016-03-17)
On irrationality of surfaces in $\mathbb{P}^3$