A NEW CURVE ALGEBRAICALLY BUT NOT RATIONALLY UNIFORMIZED BY RADICALS

作者：Pirola Gian Pietro^*; Rizzi Cecilia; Schlesinger Enrico

来源：Asian Journal of Mathematics, 2014, 18(1): 127-141.

DOI：10.4310/ajm.2014.v18.n1.a7

• Monodromy groups
• Galois groups
• projective curves

We give a new example of a curve C algebraically, but not rationally, uniformized by radicals. This means that C has no map onto P-1 with solvable Galois group, while there exists a curve C' that maps onto C and has a finite morphism to P-1 with solvable Galois group. We construct such a curve C of genus 9 in the second symmetric product of a general curve of genus 2. It is also an example of a genus 9 curve that does not satisfy condition S(4,2,9) of Abramovich and Harris.

• 出版日期2014-1