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3 questions
7
votes
1
answer
543
views
A constructive proof of the theorem of the cube
Do you know a constructive proof of the theorem of the cube ? More precisely, let $X$, $Y$, $Z$ be projective varieties (e.g., over an algebraically closed field $k$) with points $x$, $y$, $z$ ...
- 28.8k
4
votes
1
answer
169
views
Tri-homogenous polynomials of tridegree $(3,3,3)$ to add three points on an elliptic curve
Consider an elliptic curve $E \subset \mathbb{P}^2$ with the zero point $\mathcal{O}$. There are classical articles about complete systems of addition laws on $E$ (see
Lange and Ruppert - Complete ...
- 20.8k
3
votes
2
answers
396
views
Abelian varieties corresponding to Hodge substructures
In an exercise of Voisin book, says:
Let $j:C\rightarrow S$ the inclusion of a smooth curve on a smooth connected projective surface. Set
$H=ker(j_*:H^1(C,\mathbb{Z})\rightarrow H^3(S,\mathbb{Z}))$.
...
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