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Results tagged with projective-varieties
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user 38823
In algebraic geometry, a projective variety over an algebraically closed field $k$ is a subset of some projective $n$-space $\mathbb P^n$ over $k$ that is the zero-locus of some finite family of homogeneous polynomials of $n + 1$ variables with coefficients in $k$, that generate a prime ideal, the defining ideal of the variety
1
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0
answers
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Canonical bundle formula for CY fibration over $\mathbb P^1$ without multiple fibers
Let us call a smooth projective vartiety $M$ as Calabi-Yau (CY) manifold if it has trivial canonical class and
$h^i(M, \mathcal O_M ) = 0$ for $0 < i < \dim(M)$.
In this definition, a CY 1-fold is an …
- 1,841
2
votes
0
answers
291
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Hypersurfaces in projective bundles over $\mathbb P^1$
I am working on a suggestion of a comment here.
Let $E \rightarrow \mathbb P^1$ be a non-trivial vector bundle of rank $r$ with $\deg E =0$ and $\mathbb P(E) \rightarrow \mathbb P^1$ be its projectiz …
- 1,841
6
votes
2
answers
441
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CY fibration over $\mathbb P^1$ without any singular fibers
Let's call a smooth projective vartiety $M$ as Calabi-Yau (CY) manifold if it has trivial canonical class and
$h^i(M, \mathcal O_M ) = 0$ for $0 < i < \dim(M)$.
In this definition, a CY 1-fold is an e …
- 1,841
3
votes
1
answer
429
views
Examples of CY fibrations over $\mathbb P^1$
We work over $\mathbb C$ and let us call a smooth projective vartiety $M$ as Calabi-Yau (CY) manifold if it has trivial canonical class and
$h^i(M, \mathcal O_M ) = 0$ for $0 < i < \dim(M)$.
In this d …
- 1,841
3
votes
1
answer
231
views
Irrationality of some threefolds
Consider a smooth projective threefold $\overline W$, constructed in section 4 of this paper.
This threefold is a resolution of singularities of the quotient of a product of a K3 surface and $\mathbb …
- 1,841