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Results tagged with ag.algebraic-geometry
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user 478525
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
6
votes
2
answers
422
views
Good and bad reduction for twists of algebraic curves
Suppose we have two curves $C/\mathbb{Q}$ and $C'/\mathbb{Q}$ which are twists of each other i.e. they are isomorphic over a field extension $K/\mathbb{Q}$.
Suppose that $C$ has good reduction at a pr …
- 637
2
votes
0
answers
178
views
Automorphisms of a K3 surface
I was studying the following algebraic surface in $\mathbb{P}^5$ defined by the following three quadrics:
\begin{cases}
x^2 + xy + y^2=w^2\\
x^2 + 3xz + z^2=t^2\\
y^2 + 5yz + z^2=s^2.
…
- 637
6
votes
1
answer
480
views
Flatness of schemes
I am learning about flatness for the first time and I cannot wrap my head around why the definition with tensor products of a flat module implies geometrically that 1-parameter families of schemes hav …
- 28.7k
2
votes
0
answers
191
views
rational curves over K3 surfaces over $\mathbb{Q}$
There are many partial results towards the following conjecture:
Every projective K3 surface over an algebraically closed field contains infinitely many integral rational curves.
My question is: is th …
- 637