Journal of the Ramanujan Mathematical Society

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A Criterion for M-Curves


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1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India
     

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We prove that a geometrically irreducible smooth projective curve X of genus g>1 defined over ℝ is an M-variety if and only if Pic0(X) is an M-variety. A geometrically irreducible smooth projective curve X defined over ℝ is an M-variety if and only if Pic1(X) is an M-variety; note that there is no condition on the genus.
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  • A Criterion for M-Curves

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Authors

Indranil Biswas
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India
Shane D’Mello
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India

Abstract


We prove that a geometrically irreducible smooth projective curve X of genus g>1 defined over ℝ is an M-variety if and only if Pic0(X) is an M-variety. A geometrically irreducible smooth projective curve X defined over ℝ is an M-variety if and only if Pic1(X) is an M-variety; note that there is no condition on the genus.