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1
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On stable conjugacy of finite subgroups of the plane Cremona group, I

100%
Bogomolov F., Prokhorov Y.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2099-2105
EN
We discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We compute the stable birational invariant H 1(G, Pic(X)) for cyclic groups of prime order.
2
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Towards the classification of weak Fano threefolds with ρ = 2

61%
Cutrone J., Marshburn N.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1552-1576
EN
In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases is proven.
3
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Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

52%
Trepalin A.
Open Mathematics
|
2014
|
tom 12
|
nr 2
229-239
EN
Let $$\Bbbk$$ be a field of characteristic zero and G be a finite group of automorphisms of projective plane over $$\Bbbk$$. Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field $$\Bbbk$$ is algebraically closed. In this paper we prove that $${{\mathbb{P}_\Bbbk ^2 } \mathord{\left/ {\vphantom {{\mathbb{P}_\Bbbk ^2 } G}} \right. \kern-\nulldelimiterspace} G}$$ is rational for an arbitrary field $$\Bbbk$$ of characteristic zero.
4
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Halphen pencils on weighted Fano threefold hypersurfaces

52%
Cheltsov I., Park J.
Open Mathematics
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2009
|
tom 7
|
nr 1
1-45
EN
On a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.
5
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Weakly-exceptional quotient singularities

42%
Sakovics D.
Open Mathematics
|
2012
|
tom 10
|
nr 3
885-902
EN
A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.
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