Covering gonalities of complete intersections in positive characteristic

Abstract

We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery for complex varieties. We show that over an arbitrary field a smooth multidegree $(d_1,\dots ,d_k)$ complete intersection in ${\mathbb{P}}^N$ has separable covering gonality at least $d-N+1$, where $d=d_1+\cdots +d_k$. We also show that the very general such variety has covering gonality at least $\frac{d-N+2}{2}$.

13 pages

References in corpus (4)

• Measures of irrationality for hypersurfaces of large degree
• Gonality of curves on general hypersurfaces
• Rational curves on general type hypersurfaces
• Chow rings and gonality of general abelian varieties

Cited by in corpus (1)

• Multiplicative bounds for measures of irrationality on complete intersections