Benjamin Church

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math.AG2025

Obstructions to unirationality for product-quotient surfaces over $F_{p}$

Benjamin Church

We construct a surface over $F_{p}$ with $π_{1}^{e ˊ t} (X) = 1$ that is supersingular -- in the sense that $H_{e ˊ t}^{2} (X, Q_{ℓ} (1))$ is spanned by algebraic…

math.AG2025

Nowhere vanishing 1-forms on 4-folds

Benjamin Church

In this note, we prove -- in dimension at most 4 -- a conjectue of Hao which says that a morphism $f : X \to A$ to a simple abelian variety $A$ is smooth if and only if there is a…

math.AG2024

Nowhere vanishing 1-forms on varieties admitting a good minimal model

Benjamin Church

We prove several conjectures relating the existence of nonvanishing 1- forms to smooth morphisms over abelian varieties, assuming the existence of good minimal models. The proof in…

Obstructions to unirationality for product-quotient surfaces over Fp​

Nowhere vanishing 1-forms on 4-folds

Nowhere vanishing 1-forms on varieties admitting a good minimal model

Obstructions to unirationality for product-quotient surfaces over $F_{p}$