UnirationalHurwitzSchemes -- Unirationality of some Hurwitz schemes

This package implements the methods of the paper 'The unirationality of the Hurwitz schemes H_10,8 and H_13,7' and serves as supporting code for the computational proofs it contains. The code needed to verify all the assertions of the paper is provided, as well as an output of its execution.

Auxiliary functions

• isSmooth -- check whether an ideal defines a smooth curve in P1*P2
• isOrdDoublePoints -- check whether a curve in P1*P2 has at worst ordinary double points as singularities
• genusP1P2 -- computes the genus of a curve embedded in P1*P2

Main functions

• random8gonalGenus10Curve -- a general 8-gonal genus 10 curve in P1*P2
• randomGenus10CurveNMarkedPoints -- a general genus 10 curve in P1*P2, with N marked points on it
• randomGenus13Degree17CurveInP6 -- a general genus 13 curve of degree 17 in P6
• randomGenus12Degree14CurveInP4 -- a general genus 12 curve of degree 14 in P4
• randomGenus13Degree7CoverOfP1 -- a general canonical curve of genus 13 with a g^1_7
• randomGenus12Degree8CoverOfP1 -- a general canonical curve of genus 12 with a g^1_8
• randomGenus10Degree8CoverOfP1 -- a general canonical curve of genus 10 with a g^1_8

Verify all the assertions of the paper

• verifyAssertionsOfThePaper -- print commands to verify the assertions of the paper

This package requires Macaulay2 Version 1.10 or newer