All Questions
Tagged with fano-varieties birational-geometry
11 questions
1
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98
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Geometry of destabilizing centers in $K$-stability
In $K$-stability destabilizing centers are, roughly speaking, centers of valuations computing the stability thresholds.
It is known that if $X$ is non $K$-semistable Fano variety then there exists a ...
- 8,998
5
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0
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260
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Equations for conic del Pezzo surfaces of degree one
Let $X$ be a del Pezzo surface of degree one over a field $k$ of characteristic not $2$ equipped with a conic bundle $\pi: X \rightarrow \mathbb{P}^1$. By Theorem 5.6 of this paper, $X$ admits a ...
- 241
2
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1
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353
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Cohomology of normal bundle and tangent bundle on Gushel-Mukai threefold
Let $X$ be a smooth general ordinary Gushel-Mukai threefold. There is an embedding $X\rightarrow\mathrm{Gr}(2,5):=G$. Consider the normal bundle $\mathcal{N}_{X|G}$, how to compute cohomology of this ...
- 1,982
3
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150
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How to distinguish the singularities on moduli space?
Let me start with concrete examples. Let $X$ be a smooth special Gushel-Mukai threefold and $\mathcal{C}(X)$ be its honest Fano surface of conics, it has two irreducible components $\mathcal{C}(X)=\...
- 1,982
6
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3
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868
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Pseudo-automorphisms on Fano varieties
Is every pseudo-automorphism (self-birational map which does not contract any hypersurface) of a smooth Fano variety of Picard rank $1$ equal to a biregular automorphism?
Remark: For $\mathbb{P}^n$, ...
- 7,722
1
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0
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88
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Is there a direct way to show Fano surface of lines and conics on the pairs of Fano threefolds isomorphic?
I am considering the following setting:
Let $(Y_d, X_{4d+2})$ be the pair of degree $d$ and index 2 Fano threefold $Y_d$ and degree $4d+2$ index 1 Fano threefold and both of them are Picard number 1. ...
- 1,982
5
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1
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585
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Anti-canonical divisor of a Fano variety
Let $X$ be a normal projective Fano variety, that is the anti-canonical divisor $-K_X$ is ample.
For any $m>0$ let us consider the complete linear system $|-mK_X|$ and the map
$$f_{|-mK_X|}:X\...
user101890
5
votes
1
answer
162
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Rationality of $V_1$ fano threefold
In the book of Iskovskikh and Prokhorov it seems not known wether the $V_1$, an hypersurface of degree $6$ in the weighted projective space $\mathbb{P}(3,2,1,1,1)$, is rational or not. Is there any ...
- 382
5
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3
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3k
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Weak Fano and Log fano varieties
A projective smooth variety $X$ is weak Fano if $-K_X$ is nef and big. We say that $X$ is log Fano is there exists a divisor $D$ such that $-(K_X+D)$ is ample and $(X,D)$ is Kawamata log terminal.
Is ...
user49214
1
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1
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503
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Reference request: log Fano varieties
I need a reference for a proof of the following fact: let $X$ be a toric variety then $X$ is log Fano.
Thanks a lot.
user58018
3
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1
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310
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Are weak Fano 4-folds with canonical Gorenstein singularities bounded?
A Fano variety over $\mathbb{C}$ with Gorenstein singularity is called weak Fano if the anti-canonical divisor is nef and big.
Are there finite families of weak Fano 4-folds with canonical ...
- 3,472