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for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.

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What does Hodge theory tell us about simply connected surfaces of general type

Let $X$ be a smooth complex projective variety. We know that $\Omega^1_X$ has a non-zero section if and only if the abelianization of the fundamental group of X is infinite. This follows from Hodge th …
Fabiano Rug's user avatar