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Results tagged with ag.algebraic-geometry
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user 4140
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
12
votes
Accepted
How does one know the following surface contains no other lines?
A line is given by a pair of equations:
\begin{equation*}
a_1 x_1 +a_2 x_2+a_3 x_3 + a_4 x_4=0, \qquad
b_1 x_1 + b_2 x_2 + b_3 x_3 + b_4 x_4=0.
\end{equation*}
Suppose this line is on $X$.
If the mi …
- 3,142
4
votes
1
answer
196
views
Smooth real points on the intersection of a quadric and a cubic
Let $C$, $Q \in \mathbb{R}[x_0,\dots,x_n]$ be homogeneous of degrees $3$ and $2$ respectively. Consider the scheme $V$ in $\mathbb{P}^n$ defined by
$$ V \; : \; C=Q=0$$.
Suppose
$V$ is integral (ove …
- 3,142
5
votes
1
answer
416
views
Certain double covers of cubic surfaces
Let $S$ be a smooth cubic surface in $\mathbb{P}^3$. I would like to understand that variety $V$ that parametrizes lines $\ell$ such that $\ell \cdot S=3P$ with $P \in S$. At any point $P \in S$, let …
- 3,142
10
votes
Rational points on surfaces of general type
A Theorem of Faltings states that any proper subvariety of an abelian variety has finitely many rational points provided this subvariety does not contain a translate of any non-trivial proper abelian …
- 3,142