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Results tagged with grothendieck-riemann-roch
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user 153853
The Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds, which is itself a generalisation of the classical Riemann–Roch theorem for line bundles on compact Riemann surfaces.
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Can the dimension of Hom space between vector bundles on an algebraic curve predicted by Rie...
Let us study vector bundles $E$ and $F$ on a smooth projective curve $C$. There is a Riemann-Roch type formula for the Euler characteristic $\chi(E,F)=dim\, Hom(E,F)-dim\, Ext^1(E,F)$ in terms of degr …
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Can the dimension of Hom space between vector bundles on an algebraic curve predicted by Rie...
I have found the answer, it is positive.
The statement is equivalent to a theorem of Hirschowitz, see Th. 1.2 in arXiv:alg-geom/9710019v2.