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

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Restriction of a dominant map to a hypersurface

Suppose there is a dominant morphism $H: \mathbb{A}^1_k \times W \to X$ such that $H(0, -) \neq H(1, -)$ as morphisms from $W$ to $X$. Here $W$ and $X$ are varieties over a field $k$. Assume that $di …