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$M$-curve; symmetric product; real locus

Let $(X , \sigma)$ be a geometrically irreducible smooth projective $M$-curve of genus $g$ defined over the field of real numbers.We prove that the $n$-th symmetric product of $(X , \sigma)$ is an $M$-variety for $n$ = 2 ,3 and $n \geq 2g − 1$.

INDRANIL BISWAS¹ SHANE D’MELLO²

1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
2. Department of Mathematics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India

Published

1 September 2017

Manuscript received

8 May 2015

Manuscript revised

24 February 2016

Accepted

1 March 2016

Early published

Unedited version published online

Final version published online

3 August 2017