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LSpice
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Noether folrmula, Riemann Roch , Reimann Surfaces, Global Dimension of global holomorphic sections of a Lineline bundle

Let K$K$ be the canonical line bundle of a compact Riemann Surface Msurface $M$ of genus g $g$. Consider the pull back of K$K$ on M x M via$M \times M$ via projection on the first factor. What is the dimension of the space of global Holomorphicholomorphic sections of this pull back line bundle on M x M$M \times M$?

I can calculate its Euler Characteristiccharacteristic by Riemann-RochRiemann–Roch ( Noether’sNoether’s formula), but how does one calculate H^0$H^0$?

Thank you,

Noether folrmula, Riemann Roch , Reimann Surfaces, Global holomorphic sections of a Line bundle

Let K be the canonical line bundle of a compact Riemann Surface M of genus g . Consider the pull back of K on M x M via projection on the first factor. What is the dimension of the global Holomorphic sections of this pull back line bundle on M x M?

I can calculate its Euler Characteristic by Riemann-Roch( Noether’s formula) but how does one calculate H^0?

Thank you,

Dimension of global holomorphic sections of a line bundle

Let $K$ be the canonical line bundle of a compact Riemann surface $M$ of genus $g$. Consider the pull back of $K$ on $M \times M$ via projection on the first factor. What is the dimension of the space of global holomorphic sections of this pull back line bundle on $M \times M$?

I can calculate its Euler characteristic by Riemann–Roch (Noether’s formula), but how does one calculate $H^0$?

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Roch
Roch
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Noether folrmula, Riemann Roch , Reimann Surfaces, Global holomorphic sections of a Line bundle

Let K be the canonical line bundle of a compact Riemann Surface M of genus g . Consider the pull back of K on M x M via projection on the first factor. What is the dimension of the global Holomorphic sections of this pull back line bundle on M x M?

I can calculate its Euler Characteristic by Riemann-Roch( Noether’s formula) but how does one calculate H^0?

Thank you,