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Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 02/2019, Volume 2019, Issue 747, pp. 147 - 174
Let be a complex rational cuspidal curve and let be the minimal log resolution of singularities. We prove that has at most six cusps and we establish an... 
MATHEMATICS | Mathematics - Algebraic Geometry
Journal Article
Mathematische Annalen, ISSN 0025-5831, 8/2015, Volume 362, Issue 3, pp. 1107 - 1142
We provide a complete classification of Fano threefolds $$X$$ X having canonical Gorenstein singularities and anticanonical degree $$(-K_{X})^{3} = 64$$ ( - K... 
Mathematics, general | Mathematics | 14J45 | 14E30 | 14J17 | MATHEMATICS
Journal Article
The Michigan mathematical journal, ISSN 0026-2285, 03/2013, Volume 62, Issue 1, pp. 3 - 37
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 1/2016, Volume 203, Issue 1, pp. 303 - 331
Let $$X$$ X be an algebraic variety of characteristic zero. Terminal valuations are defined in the sense of the minimal model program, as those valuations... 
Mathematics, general | Mathematics | Secondary 14E30 | 14J17 | Primary 14E18 | MATHEMATICS | VARIETIES | GERMS | IMAGE | SPACES | ARC FAMILIES | Valuation | Analysis | Theorems | Algebra | Theorem proving | Images | Texts | Mathematical models | Terminals | Formulas (mathematics) | Mathematics - Algebraic Geometry
Journal Article
Osaka Journal of Mathematics, ISSN 0030-6126, 03/2012, Volume 49, Issue 1, pp. 225 - 245
For normal two dimensional hypersurface singularities of Brieskorn type, concrete descriptions are given to both the fundamental cycle and the maximal ideal... 
MATHEMATICS | ELLIPTIC-SINGULARITIES | 32S25 | 14J17
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 3/2017, Volume 207, Issue 3, pp. 1239 - 1287
For a germ f on a complex manifold X, we introduce a complex derived from the Liouville form acting on logarithmic differential forms, and give an exactness... 
14N20 | 32S22 | 14F40 | 14J17 | 58A10 | Mathematics, general | 14F10 | 13D45 | Mathematics | 32C38
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 05/2007, Volume 138, Issue 1, pp. 119 - 136
We prove the rational connectedness conjecture of V. V. Shokurov in [20] which, in particular, implies that the fibres of a resolution of a variety with... 
MATHEMATICS | VARIETIES | 14J45 | 14E30 | 14E05 | 14J17
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 10/2017, Volume 287, Issue 1, pp. 361 - 403
We develop a theory of local densities and tangent cones in a motivic framework, extending work by Cluckers–Comte–Loeser about p-adic local density. We prove... 
11S80 | 12J10 | 14J17 | Henselian valued fields | Mathematics | Regular stratification | 14B05 | Local density | 32Sxx | Mathematics, general | Motivic integration | Primary 03C98 | Secondary 03C68 | MATHEMATICS | ZETA-FUNCTIONS | INTEGRATION | CELL DECOMPOSITION | DEFINABLE SETS | STRATIFICATIONS | SUBANALYTIC SETS
Journal Article
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, ISSN 0025-5645, 01/2018, Volume 70, Issue 1, pp. 387 - 402
Let f(II)(z, (z) over bar) = z(1)(a1+b1)(z) over bar (-b1)(1)z(2) + ... + z(n-1)(an-1+bn-1)(z) over bar (bn-1)(n-1)z(n) + z(n)(an+bn)(z) over bar (-bn-)(n)z(1)... 
MATHEMATICS | Milnor fibration | polar weighted homogeneous
Journal Article
Mathematische Annalen, ISSN 0025-5831, 7/2011, Volume 350, Issue 3, pp. 721 - 754
Montgomery–Yang problem predicts that every pseudofree circle action on the 5-dimensional sphere has at most 3 non-free orbits. Using a certain one-to-one... 
Mathematics, general | 14J17 | Mathematics | MATHEMATICS | QUOTIENTS | SURFACES
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2013, Volume 41, Issue 11, pp. 4333 - 4338
Elementary examples are presented of normal algebraic surfaces X with singular points x such that at the local ring X, x there exist Azumaya algebras of all... 
Class group | Rational surface | Azumaya algebras | Brauer group | Non rational singularity | Secondary 14F22, 14J17, 14J26 | Secondary 14F22 | 14J26 | MATHEMATICS | 16H05 | 14J17 | Algebra
Journal Article
Mathematische Annalen, ISSN 0025-5831, 10/2016, Volume 366, Issue 1, pp. 141 - 166
We introduce the notion of potentially klt pairs for normal projective varieties with pseudoeffective anticanonical divisor. The potentially non-klt locus is a... 
14M22 | Mathematics, general | Mathematics | 14J45 | Primary 14E30 | Secondary 14J17 | MATHEMATICS | BASE LOCI | COX RINGS | SINGULARITIES | VARIETIES | FANO MANIFOLDS | CONE | RATIONAL CONNECTEDNESS
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 09/2013, Volume 62, Issue 3, pp. 475 - 489
Journal Article
Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 2016, Volume 92, Issue 1, pp. 13 - 18
We prove that the class of log canonical rational singularities is closed under the basic operations of the minimal model program. We also give some... 
Rational singularities | Minimal model program | Log canonical singularities | Log canonical surfaces | MATHEMATICS | log canonical singularities | minimal model program | log canonical surfaces | SURFACES | Singularities (Mathematics) | Analysis | Theoretical mathematics | Mathematical models | Singularities | Series (mathematics) | 14E30 | 14J17
Journal Article
Acta Mathematica Vietnamica, ISSN 0251-4184, 3/2019, Volume 44, Issue 1, pp. 87 - 100
In this paper, we give a formula for normal reduction number of an integrally closed m $\mathfrak m$ -primary ideal of a two-dimensional normal local ring ( A... 
Normal reduction number | 14J17 | Mathematics, general | Mathematics | 13B22 | Geometric genus | Hypersurface of Brieskorn type | Secondary 14B05
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2019, Volume 291, Issue 3, pp. 905 - 930
This work has two complementary parts, in the first part we compute the local Euler obstruction of generic determinantal varieties and apply this result to... 
Chern–Schwartz–MacPherson class | Primary 14C17 | Stabilization | 58K05 | 32S60 | Mathematics | Generic determinantal varieties | 55S35 | Essentially isolated determinantal singularity | Local Euler obstruction | Secondary 14J17 | Mathematics, general | 32S15 | MATHEMATICS | Chern-Schwartz-MacPherson class | FORMULA | EQUISINGULARITY | POLAR MULTIPLICITIES | INDEXES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 12/2014, Volume 267, pp. 1 - 43
Let E⊆P2 be a complex rational cuspidal curve contained in the projective plane and let (X,D)→(P2,E) be the minimal log resolution of singularities. Applying... 
Cuspidal curve | Rational curve | Coolidge–Nagata conjecture | Cremona transformation | Log Minimal Model Program | Coolidge-Nagata conjecture | MATHEMATICS | HOMOLOGY PLANES | CURVES | Mathematics - Algebraic Geometry
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2012, Volume 161, Issue 8, pp. 1455 - 1520
We introduce a notion of volume of a normal isolated singularity that generalizes Wahl's characteristic number of surface singularities to arbitrary... 
MATHEMATICS | MODELS | VARIETIES | PLURIGENERA | VALUATION | MULTIPLIER IDEALS | ENDOMORPHISMS | RATIONAL SURFACES | ASYMPTOTIC-BEHAVIOR | Mathematics - Algebraic Geometry | 14F18 | 14E99 | 14C20 | 14J17
Journal Article
ALGEBRA & NUMBER THEORY, ISSN 1937-0652, 2019, Volume 13, Issue 2, pp. 425 - 454
We study pushforwards of log pluricanonical bundles on projective log canonical pairs. (Y, Delta) over the complex numbers, partially answering a Fujita-type... 
MATHEMATICS | pluricanonical bundles | Fujita's conjecture | weak positivity | VARIETIES | Seshadri constants | effective results
Journal Article
Osaka Journal of Mathematics, ISSN 0030-6126, 03/2009, Volume 46, Issue 1, pp. 291 - 316
We study the boundary L-t of the Milnor fiber for the non-isolated singularities in C-3 With equation z(m) - g(x, y) = 0 where m >= 2 and g(x, y) = 0 is a... 
TOPOLOGY | MATHEMATICS | Mathematics | 32S25 | 14J17 | 57M25
Journal Article
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