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

5 votes
1 answer
249 views

Does this extension of Hodge structures split over $\mathbb{Q}$?

Let $X$ be a smooth projective curve of genus $\geq 1$ over $\mathbb{C}$, $H^\cdot=H^\cdot(X)$, and $K$ be the kernel of cup product $\cup: H^1\otimes H^1\rightarrow H^2$. Consider the extension of Ho …
P.E.'s user avatar
  • 299
0 votes
0 answers
1k views

Chow group of a product

Let $X$ and $Y$ be smooth varieties over $k$. I was wondering if there is a decomposition of the Chow group $CH(X\times Y)$ in terms of $CH(X)$ and $CH(Y)$ similar to the Kunneth decomposition of $H(X …
P.E.'s user avatar
  • 299
-1 votes
1 answer
97 views

How to prove embedded copies of a curve using different base points in its Jacobian are alge...

Let $X$ be a smooth projective curve over $k\subset\mathbb{C}$, and $p,q\in X(k)$. Let $X_p$ (resp. $X_q$) be the embedded copy of $X$ in the Jacobian $Jac(X)$ using the base point $p$ (resp. $q$). Is …
P.E.'s user avatar
  • 299