All Questions
Tagged with fano-varieties complex-geometry
11 questions
2
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1
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Fourier-Mukai functors and autoequivalence groups of $G$-equivariant derived categories
I have a few questions about $G$-equivariant derived categories. For my question, I'm assuming $G$ is cyclic. Also, in my case $G$ does not act on $X$, only on $D^b(X)$.
Q1: Orlov's Representability ...
- 305
1
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0
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93
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Fourier-Mukai kernels for Fano threefolds
Let $Y_1$ and $Y_1'$ be index two degree one Fano threefolds. Suppose we have a Fourier-Mukai equivalence $\Phi_P : \mathrm{D}^b(Y_1) \to \mathrm{D}^b(Y_1')$. Can anything be said about the kernel $P$,...
- 305
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1
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Do non-compact Fano manifolds exist?
Suppose $(M,g, \omega)$ is a Kähler manifold with $\text{Ric}(g) = g$, i.e., $M$ is a Fano manifold. Is $M$ necessarily compact? If not, perhaps complete and Fano implies compact? I'd like to build a ...
user105074
0
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1
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189
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Negative Definite Fano Manifolds
A complex manifold $M$ is said to be Fano if the Chern curvature $2$-form is a positive definite $(1,1)$-form. What happens if the Chern curvature $2$-form is a negative definite $(1,1)$-form? What ...
9
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1
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593
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Do all Fano threefolds have effective $c_2$?
Let $X$ be a smooth complex projective Fano threefold. Then the class $c_1(X)$ can be realised as an effective divisor in $X$. It is it true that the class $c_2(X)$ can be realised as an effective ...
- 14.3k
3
votes
1
answer
273
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Are varieties with negative Kodaira dimension covered by hyperkahlers
Let $X$ be a smooth projective variety with negative Kodaira dimension over $\mathbb{C}$.
Is there an integer $n\geq 1$, a smooth projective hyperkahler variety $H$, and a finite morphism $H\to X^n$?
...
- 31
5
votes
1
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344
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Fano blow ups of $\mathbb CP^n$
Let $X$ be a smooth complex variety. Is it always possible to find an embedding $\varphi: X\to \mathbb CP^n$ for some $n$, such that the blow up of $\mathbb CP^n$ at $\varphi(X)$ is a Fano variety?
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- 14.3k
1
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1
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Analogy of a Fano manifold with anticanonical divisor
Some people say that a Fano manifold with anticanonical divisor is an analogue of a manifold with boundary. Where does this intuition come from?
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11
votes
2
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760
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Families of Fano varieties over non-hyperbolic curves
Let $C$ be a non-hyperbolic (smooth quasi-projective connected complex algebraic) curve. That is, $C$ is isomorphic to $\mathbb P^1, \mathbb A^1, \mathbb G_m$, or an elliptic curve.
Let $f:X\to C$ be ...
- 9,497
4
votes
1
answer
513
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Toric Fano Kahler manifolds and Delzant polytopes
Let $P$ be a Delzant polytope in $\mathbb R^n$, given by a set of inequalities $\ell_i(x) > 0$ where $\ell_i(x) = \sum_k \mu_k^i x_k - \lambda_i$.
In his paper http://arxiv.org/abs/0803.0985 ...
- 585
3
votes
1
answer
893
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Existence of constant scalar curvature Kahler metrics on projective manifolds
It is well known that the blow-up of $\mathbb P^2$ in one or two points does not accept a Kahler-Einstein metric. Kahler-Einstein metrics are particular cases of constant scalar curvature Kahler ...
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