We show that the Hurwitz scheme Hg; d parametrizing d-sheeted simply branched covers of the projective line by smooth curves of genus g, up to isomorphism, is unirational for ðg; dÞ ¼ ð10; 8Þ and ð13; 7Þ. The unirationality is settled by using liaison constructions in P1 P2 and P6 respectively, and through the explicit computation of single examples over a finite field.
The unirationality of the Hurwitz schemes H_10,8 and H_13,7
Fabio Tanturri
2019-01-01
Abstract
We show that the Hurwitz scheme Hg; d parametrizing d-sheeted simply branched covers of the projective line by smooth curves of genus g, up to isomorphism, is unirational for ðg; dÞ ¼ ð10; 8Þ and ð13; 7Þ. The unirationality is settled by using liaison constructions in P1 P2 and P6 respectively, and through the explicit computation of single examples over a finite field.
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