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60
Multiplier ideals of monomial ideals
 Trans. Amer. Math. Soc
"... Abstract. In this note we discuss a simple algebraic calculation of the multiplier ideal associated to a monomial ideal in affine nspace. We indicate how this result allows one to compute not only the multiplier ideal but also the log canonical threshold of an ideal in terms of its Newton polygon. ..."
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Cited by 49 (1 self)
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Abstract. In this note we discuss a simple algebraic calculation of the multiplier ideal associated to a monomial ideal in affine nspace. We indicate how this result allows one to compute not only the multiplier ideal but also the log canonical threshold of an ideal in terms of its Newton polygon.
Jumping coefficients of multiplier ideals
 Duke Math. J
"... Dedicated to Y.T. Siu on the occasion of his sixtieth birthday ..."
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Cited by 34 (3 self)
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Dedicated to Y.T. Siu on the occasion of his sixtieth birthday
An interpretation of multiplier ideals via tight closure
, 2001
"... Hara [Ha3] and Smith [S2] independently proved that in a normal QGorenstein ring of characteristic p ≫ 0, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair (R, ∆) of a normal ring R and an effective QWeil divisor ∆ on Spec R. A ..."
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Cited by 15 (5 self)
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Hara [Ha3] and Smith [S2] independently proved that in a normal QGorenstein ring of characteristic p ≫ 0, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair (R, ∆) of a normal ring R and an effective QWeil divisor ∆ on Spec R. As a corollary, we obtain the equivalence of strongly Fregular pairs and klt pairs.
On the degree of Fano threefolds with canonical Gorenstein singularities, I
, 2003
"... We consider Fano threefolds X with canonical Gorenstein singularities. Under additional assumption that X has at least one noncDV point we prove a sharp bound of the degree: −K3 X ≤ 72. ..."
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Cited by 12 (2 self)
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We consider Fano threefolds X with canonical Gorenstein singularities. Under additional assumption that X has at least one noncDV point we prove a sharp bound of the degree: −K3 X ≤ 72.
Multiplier ideals, bfunction, and spectrum of a hyperplane singularity. arXiv:math.AG/0402363
, 2006
"... Abstract. We prove that certain roots of the BernsteinSato polynomial (i.e. bfunction) are jumping coefficients up to a sign, showing a partial converse of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith, and D. Varolin. We also prove that certain roots are determined by a filtration on the Milnor ..."
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Cited by 8 (5 self)
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Abstract. We prove that certain roots of the BernsteinSato polynomial (i.e. bfunction) are jumping coefficients up to a sign, showing a partial converse of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith, and D. Varolin. We also prove that certain roots are determined by a filtration on the Milnor cohomology, generalizing a theorem of B. Malgrange in the isolated singularity case. This implies a certain relation with the spectrum which is determined by the Hodge filtration, because the above filtration is related to the pole order filtration. For multiplier ideals we prove an explicit formula in the case of locally conical divisors along a stratification, generalizing a formula of Mustat¸ǎ in the case of hyperplane arrangements. For the bfunction of a generic hyperplane arrangement, we determine the multiplicity of −1 and complete a formula of U. Walther.
Logarithmic orbifold Euler numbers of surfaces with applications, math.AG/ 0012180
, 2000
"... If X is a quasiprojective variety with only isolated quotient singularities then one can define an orbifold Euler number of X as eorb(X) = etop(X) − ..."
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Cited by 8 (0 self)
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If X is a quasiprojective variety with only isolated quotient singularities then one can define an orbifold Euler number of X as eorb(X) = etop(X) −
Threefold Thresholds
"... We prove that the set of accumulation points of thresholds in dimension three is equal to the set of thresholds in dimension two, excluding one. ..."
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Cited by 7 (1 self)
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We prove that the set of accumulation points of thresholds in dimension three is equal to the set of thresholds in dimension two, excluding one.
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 7 (1 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
BernsteinSato polynomials of hyperplane arrangements
"... Abstract. Using a generalization of Malgrange’s formula and a solution of Aomoto’s conjecture due to Esnault, Schechtman and Viehweg, we calculate the BernsteinSato polynomial (i.e. bfunction) of a hyperplane arrangement with a reduced equation, and show that its roots are greater than −2 and the ..."
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Cited by 7 (4 self)
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Abstract. Using a generalization of Malgrange’s formula and a solution of Aomoto’s conjecture due to Esnault, Schechtman and Viehweg, we calculate the BernsteinSato polynomial (i.e. bfunction) of a hyperplane arrangement with a reduced equation, and show that its roots are greater than −2 and the multiplicity of −1 coincides with the (effective) dimension. As a corollary we get a new proof of Walther’s formula for generic central hyperplane arrangements.
Classification of threedimensional exceptional log canonical hypersurface singularities
 II // Izv. Math. 2004. V
"... Abstract. In this paper the threedimensional exceptional strictly log canonical hypersurface singularities are described and the detailed classification of threedimensional exceptional canonical hypersurface singularities is given under the condition of wellformedness. ..."
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Cited by 6 (5 self)
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Abstract. In this paper the threedimensional exceptional strictly log canonical hypersurface singularities are described and the detailed classification of threedimensional exceptional canonical hypersurface singularities is given under the condition of wellformedness.