Search Results

(For the record, I am summarizing the comments here.) Deligne and Fulton have shown that fundamental group of the complement of a nodal curve in $\mathbb{C}\mathbb{P}^2$ is abelian. It follows easily …

Since you are asking about Higgs bundles, I can say a few words here. These were introduced by Hitchin in the mid 1980's, although I'm not sure he used this term. One can look at the introduction …

(This would a comment, but it's hard to squeeze all the notation into the comment box.) If you are comfortable with sheaf theory, then you can use the exact sequence $$0\to \mathbb{C}\to \mathcal{O}_X …

In fact: Theorem: Any finite group $G$ is the automorphism group of a compact Riemann surface, and more generally a smooth projective algebraic curve over any algebraically closed field. The Riemann …

I have seen "big monodromy" used before, in some papers of Katz I think, with a somewhat different meaning (basically that $H^0$ should as big as possible). But I'll use your definition, since that's …

Kodaira's examples have index $\tau>0$. If $M\to S$ were isotrivial, then it is not hard to see that after pulling back to a finite unramified cover of $S$, the surface becomes a product. But this wou …