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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

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Surjective and injective criteria via Hilbert polynomials

Let $X$ be a projective complex manifold. Is it true that any coherent sheaf $\mathcal{E}$ on $X$ whose Hilbert polynomial is a constant has a surjective morphsim $\mathcal{O}_X\rightarrow \mathcal{M} …