By Riemann-Roch, for a degree 1 line bundle on a genus 2 Riemann surface the space of global holomorphic sections has dimension between $0$ and $2$. Can someone show an explicit example of a degree 1 line bundle without global (non identically vanishing) sections? (or a proof/reference that a degree 1 line bundle on a genus 2 surfaces always has a non trivial global section)
2026-03-25 19:03:44.1774465424
Line bundle of degree 1 on a genus 2 surface without global holomorphic sections
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