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Log canonical thresholds of certain Fano hypersurfaces
"... Abstract. We study log canonical thresholds on quartic threefolds, quintic fourfolds, and double spaces. As an application, we show that they have a KählerEinstein metric if they are general. All varieties are defined over C. 1. Introduction. 1.1. Introduction. The multiplicity of a nonzero polynom ..."
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Cited by 12 (8 self)
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Abstract. We study log canonical thresholds on quartic threefolds, quintic fourfolds, and double spaces. As an application, we show that they have a KählerEinstein metric if they are general. All varieties are defined over C. 1. Introduction. 1.1. Introduction. The multiplicity of a nonzero polynomial f ∈ C[z1, · · ·,zn] at a point P ∈ Cn is the nonnegative integer m such that f ∈ mm P \ mm+1
ON SINGULAR CUBIC SURFACES
, 2007
"... We study global log canonical thresholds of cubic surfaces with canonical singularities, and we prove the existence of a Kähler–Einstein metric on two singular cubic surfaces. ..."
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Cited by 9 (1 self)
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We study global log canonical thresholds of cubic surfaces with canonical singularities, and we prove the existence of a Kähler–Einstein metric on two singular cubic surfaces.
On the αInvariants of Cubic Surfaces with Eckardt Points
, 902
"... In this paper, we show that the αm,2invariant (introduced by Tian in [21] and [22]) of a smooth cubic surface with Eckardt points is strictly bigger than 2/3. This can be used to simplify Tian’s original proof of the existence of KählerEinstein metrics on such manifolds. 1 ..."
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Cited by 7 (0 self)
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In this paper, we show that the αm,2invariant (introduced by Tian in [21] and [22]) of a smooth cubic surface with Eckardt points is strictly bigger than 2/3. This can be used to simplify Tian’s original proof of the existence of KählerEinstein metrics on such manifolds. 1
EXCEPTIONAL DEL PEZZO HYPERSURFACES
, 2009
"... We compute global log canonical thresholds of a large class of quasismooth wellformed del Pezzo weighted hypersurfaces in P(a1, a2, a3, a4). As a corollary we obtain the existence of orbifold Kähler–Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well ..."
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Cited by 7 (2 self)
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We compute global log canonical thresholds of a large class of quasismooth wellformed del Pezzo weighted hypersurfaces in P(a1, a2, a3, a4). As a corollary we obtain the existence of orbifold Kähler–Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth wellformed del Pezzo weighted hypersurfaces in P(a1, a2, a3, a4).
QUASIPLURISUBHARMONIC GREEN FUNCTIONS
, 907
"... Abstract. Given a compact Kähler manifold X, a quasiplurisubharmonic function is called a Green function with pole at p ∈ X if its MongeAmpère measure is supported at p. We study in this paper the existence and properties of such functions, in connection to their singularity at p. A full characteri ..."
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Cited by 6 (1 self)
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Abstract. Given a compact Kähler manifold X, a quasiplurisubharmonic function is called a Green function with pole at p ∈ X if its MongeAmpère measure is supported at p. We study in this paper the existence and properties of such functions, in connection to their singularity at p. A full characterization is obtained in concrete cases, such as (multi)projective spaces.
On exceptional quotient singularities
, 2009
"... We study fourdimensional and fivedimensional exceptional quotient singularities. ..."
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Cited by 5 (3 self)
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We study fourdimensional and fivedimensional exceptional quotient singularities.