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Results tagged with ag.algebraic-geometry
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user 516304
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
6
votes
2
answers
320
views
Toric varieties as hypersurfaces of degree (1, ..., 1) in a product of projective spaces
I wonder if some hypersurfaces of multi-degree $(1, ..., 1)$ in a product of projective spaces are toric, with polytope a union of polytopes of toric divisors of the ambient space. This question is mo …
- 6,995
1
vote
1
answer
340
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Three-dimensional analogues of Hirzebruch surfaces
There are several ways of describing a Hirzebruch surface, for example as the blow-up of $\mathbb{P}^2$ at one point or as $\mathbb{P}(\mathcal{O}_{\mathbb{P}^1} \oplus \mathcal{O}_{\mathbb{P}^1}(n))$ …
- 549
0
votes
0
answers
138
views
Embedding of the first Hirzebruch surface in $\mathbb{P}^4$ as a cubic surface
The first Hirzebruch surface (the blow-up of $\mathbb{P}^2$ at one point) is a projective toric surface that naturally embeds into $\mathbb{P}^4$ as a cubic surface (sometimes called the cubic scroll) …
- 183
1
vote
0
answers
71
views
Embedding toric varieties in other toric varieties as a real algebraic hypersurface
In the question On a Hirzebruch surface, I've seen that the $n$-th Hirzebruch surface is isomorphic to a surface of bidegree $(n,1)$ in $\mathbb{P}^1\times \mathbb{P}^2$. I am trying to answer the fol …
- 183