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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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Existence of solutions to quadratic vector equation

Given $$A_{i,j,k} X_j^* X_k + C_i = 0$$ where $𝐴_{i,j,k}$ and $𝐶_i$ are arbitrary complex numbers for all $𝑗, 𝑘$ which are $𝑁$-dimensional indices and $i$ which is an $m$-dimensional index where …