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Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2017, Volume 221, Issue 7, pp. 1645 - 1690
We give a detailed construction of the operation “intersection with a pseudo-divisor” in algebraic cobordism, expanding on the treatment given in [8, Chapter... 
MATHEMATICS | MATHEMATICS, APPLIED | DESINGULARIZATION
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 04/2018, Volume 222, Issue 4, pp. 818 - 827
We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for... 
MATHEMATICS | GENERAL NERON DESINGULARIZATION | MATHEMATICS, APPLIED
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 04/2018, Volume 222, Issue 4, pp. 868 - 888
We prove that the moduli spaces of rational curves of degree at most 3 in linear sections of the Grassmannian Gr(2,5) are all rational varieties. We also study... 
MATHEMATICS | MATHEMATICS, APPLIED | HOMOGENEOUS VARIETIES | BUNDLES | STABLE MAPS | DESINGULARIZATION | THREEFOLD
Journal Article
Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 473 - 596
The category DA1(S) of relative cohomological 1-motives is the localizing subcategory of the triangulated category DA(S):=DAe´t(S,Q) of relative Voevodsky... 
Mixed motives | 1-motives | Voevodsky motives | Six operations formalism | MATHEMATICS | DESINGULARIZATION | CURVES | SHEAVES
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2019, Volume 267, Issue 12, pp. 7313 - 7368
Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the... 
Blow-up solutions | Extinction | Desingularization | Compacton traveling wave | Center manifolds | Quenching | SYSTEM | MATHEMATICS | PROFILES | EQUATIONS | CONSERVATION-LAWS
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 08/2015, Volume 219, Issue 8, pp. 3604 - 3628
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a... 
MATHEMATICS | MATHEMATICS, APPLIED | DESINGULARIZATION | SINGULARITIES | Algorithms
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 03/2018, Volume 2018, Issue 736, pp. 95 - 139
The purpose of this paper is to study pro excision in algebraic -theory and cyclic homology, after Suslin–Wodzicki, Cuntz–Quillen, Cortiñas, and... 
MATHEMATICS | ZERO | COHOMOLOGY | GENERAL NERON DESINGULARIZATION | HOCHSCHILD HOMOLOGY | K-Theory and Homology | Mathematics
Journal Article
Communications in Analysis and Geometry, ISSN 1019-8385, 2017, Volume 25, Issue 5, pp. 1019 - 1061
This paper is motivated by a relatively recent work by Joyce [12-16] in special Lagrangian geometry, but the basic idea of the present paper goes back to an... 
ISOLATED CONICAL SINGULARITIES | MATHEMATICS | DESINGULARIZATION | CALIBRATED SUBMANIFOLDS | UNIQUENESS
Journal Article
Journal of algebra, ISSN 0021-8693, 2019, Volume 529, pp. 268 - 535
We prove Grothendieck's conjecture on Resolution of Singularities for quasi-excellent schemes X of dimension three and of arbitrary characteristic. This... 
Resolution of singularities | Arithmetical varieties | Blowing up | Zariski | Valuations | FIELDS | CONTACT | SMOOTHNESS | PROOF | MATHEMATICS | LOCAL UNIFORMIZATION | REDUCTION | DESINGULARIZATION | SURFACES | 3-FOLDS
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 06/2019, Volume 223, Issue 6, pp. 2598 - 2614
Let X be an algebraic variety defined over a field of characteristic zero, and let ξ∈Max_mult(X) be a point in the closed subset of maximum multiplicity of X.... 
Resolution of singularities | Rees algebras | Arc spaces | MATHEMATICS | MATHEMATICS, APPLIED | SINGULARITIES | RESOLUTION | REES-ALGEBRAS | ELIMINATION | DESINGULARIZATION | Mathematics - Algebraic Geometry
Journal Article
SIAM journal on applied dynamical systems, ISSN 1536-0040, 2018, Volume 17, Issue 3, pp. 2249 - 2288
Journal Article
Nonlinearity, ISSN 0951-7715, 04/2019, Volume 32, Issue 5, pp. 1882 - 1904
The vortex-wave system describes the motion of a two-dimensional ideal fluid in which the vorticity includes continuously distributed vorticity, which is... 
maximization | Euler equation | desingularization | vortex-wave system | vortex patch | Kirchhoff-Routh function | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 01/2015, Volume 2015, Issue 698, pp. 1 - 54
We give conditions for the Mayer–Vietoris property to hold for the algebraic -theory of blow-up squares of toric varieties and schemes, using the theory of... 
MATHEMATICS | SIMPLICIAL PRESHEAVES | CYCLIC HOMOLOGY | RINGS | ALGEBRAIC K-THEORY | DESINGULARIZATION | F-1
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2018, Volume 50, Issue 4, pp. 649 - 662
Gabrielov's famous example for the failure of analytic Artin approximation in the presence of nested subring conditions is shown to be due to a growth... 
16W60 | 32A05 | 14B12 (primary) | 14QXX | 13F25 | 13P10 | MATHEMATICS | GENERAL NERON DESINGULARIZATION | Mathematics - Algebraic Geometry
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2018, Volume 331, pp. 627 - 719
In this work we characterize the subsets of Rn that are images of Nash maps f:Rm→Rn. We prove Shiota's conjecture and show that a subsetS⊂Rnis the image of a... 
Nash image | Drilling blow-up | Well-welded semialgebraic set | Arc-symmetric semialgebraic set | Nash path-connected semialgebraic set | Desingularization | MATHEMATICS | SETS | POLYNOMIAL IMAGES | PROJECTIONS | REGULAR IMAGES
Journal Article
SIAM journal on mathematical analysis, ISSN 1095-7154, 2019, Volume 51, Issue 2, pp. 1209 - 1237
We bring new results in the study of the asymptotic behavior of shrinking vortex pairs obtained by maximization of the kinetic energy in a 2-dimensional lake... 
EXISTENCE | MATHEMATICS, APPLIED | VORTICES | singular vortex pair | energy maximization | REARRANGEMENTS | FLOW | lake model | asymptotic behavior | MOTION | desingularization | POINTS | CONFIGURATIONS | 2 DIMENSIONS
Journal Article
Journal of symbolic computation, ISSN 0747-7171, 2019, Volume 95, pp. 217 - 237
We generalize the notions of ordinary points and singularities from linear ordinary differential equations to D-finite systems. Ordinary points and apparent... 
D-finite system | Ordinary point | Formal power series | Gröbner basis | Apparent singularity | Desingularization | Grobner basis | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Algebra | Algorithms | Differential equations
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 6/2016, Volume 283, Issue 1, pp. 275 - 299
We study birational maps among (1) the moduli space of semistable sheaves of Hilbert polynomial $$4m+2$$ 4 m + 2 on a smooth quadric surface, (2) the moduli... 
Moduli space | Fourier–Mukai transform | Birational morphism | Mathematics, general | Mathematics | 14D22 | 14F42 | Partial desingularization | 14E15
Journal Article
Advances in Mathematics, ISSN 0001-8708, 12/2012, Volume 231, Issue 5, pp. 3022 - 3053
The philosophy of this article is that the desingularization invariant together with natural geometric information can be used to compute local normal forms of... 
Resolution of singularities | Birational geometry | Desingularization invariant | Normal crossings | Normal form | MATHEMATICS | CHARACTERISTIC ZERO | DESINGULARIZATION
Journal Article
Communications in Algebra, ISSN 0092-7872, 02/2017, Volume 45, Issue 2, pp. 606 - 620
The Halphen transform of a plane curve is the curve obtained by intersecting the tangent lines of the curve with the corresponding polar lines with respect to... 
desingularization | Halphen's tranform | Degree | space curve | Halphen’s tranform | MATHEMATICS | Algebra | Tangents | Conics | Curves (geometry) | Transforms
Journal Article
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