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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
1
vote
1
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Can the Albanese map be anything?
Sorry for the vague title. This question is about the Albanese map from the variety $M$ of canonically polarized varieties to the set of abelian varieties. (The variety $M$ is not of finite type...)
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3
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0
answers
293
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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 …