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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
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
Journal of Algebra and its Applications, ISSN 0219-4988, 11/2015, Volume 14, Issue 9
Using the theory of minimal models of quasi-projective surfaces we give a new proof of the theorem of Lin-Zaidenberg which says that every topologically... 
cusp | Kodaira dimension | affine plane | Contractible curve | MATHEMATICS | MATHEMATICS, APPLIED | Q-HOMOLOGY PLANES | SURFACES | Mathematics - Algebraic Geometry
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 11/2017, Volume 166, Issue 16, pp. 3085 - 3145
Let E subset of P-2 be a complex rational cuspidal curve contained in the projective plane. The Coolidge-Nagata conjecture asserts that E is Cremona-equivalent... 
MATHEMATICS | RATIONAL CUSPIDAL CURVES | PLANE-CURVES | EQUIVALENT | SURFACES
Journal Article
Journal of Algebra, ISSN 0021-8693, 06/2016, Volume 456, pp. 207 - 249
A closed algebraic embedding of C⁎=C1∖{0} into C2 is sporadic if for every curve A⊆C2 isomorphic to an affine line the intersection with C⁎ is at least 2.... 
Complex plane | Embedding | Punctured affine line | Asymptote | Coordinates
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 05/2020, Volume 120, Issue 5, pp. 642 - 703
Let E⊆P2 be a complex curve homeomorphic to the projective line. The Negativity Conjecture asserts that the Kodaira–Iitaka dimension of KX+12D, where... 
14J26 | 14H50 | 14R25 (secondary) | 14J17 (primary) | MATHEMATICS
Journal Article
Acta Physica Polonica B, ISSN 0587-4254, 02/2016, Volume 47, Issue 2, pp. 491 - 496
In this paper, we present a complete Data Acquisition System (DAQ) together with the readout mechanisms for the J-PET tomography scanner. In general, detector... 
PLASTIC SCINTILLATORS | HIT-POSITION RECONSTRUCTION | MODEL SIGNALS | PHYSICS, MULTIDISCIPLINARY | LIBRARY | TIME | TOMOGRAPH
Journal Article
05/2019
We show that a complex planar curve homeomorphic to the projective line has at most four singular points. If it has exactly four then it has degree five and is... 
Journal Article
Israel journal of mathematics, ISSN 0021-2172, 06/2013, Volume 195, Issue 1, p. 37
A a-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for a-homology planes with smooth... 
Homology theory (Mathematics) | Singularities (Mathematics) | Research
Journal Article
Opto-electronics review, ISSN 1230-3402, 2020, Volume 28, Issue 1, pp. 1 - 7
Determining the dependence of phase difference modulations between light pulses in a modified Mach-Zehnder interferometer was used to develop an optical system... 
Mach-Zehnder interferometer | quantum sensors | PHYSICS, APPLIED | QUANTUM | optical fibre sensors | SYSTEMS | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Advances in Mathematics, ISSN 0001-8708, 12/2018, Volume 339, pp. 248 - 284
A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its étale endomorphisms are proper. We study the conjecture for Q-acyclic... 
Jacobian Conjecture | Belyi–Shabat polynomial | Étale endomorphism | Equivariant endomorphism | Q-homology plane | Pseudo-plane | MATHEMATICS | Belyi-Shabat polynomial | Etale endomorphism | Q-HOMOLOGY PLANES | SURFACES | Algebraic Geometry | Mathematics
Journal Article
Pacific journal of mathematics, ISSN 0030-8730, 08/2012, Volume 258, Issue 2, pp. 421 - 457
Journal Article
Israel journal of mathematics, ISSN 0021-2172, 2012, Volume 195, Issue 1, pp. 37 - 69
... BY Karol Palka ∗ Institute of Mathematics, University of Warsaw ul. Banacha 2, 02-097 Warsaw, Poland and Institute of Mathematics, Polish Academy of Sciences ul... 
Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | QUOTIENT | CURVES | AFFINE SURFACES | RATIONALITY | Mathematics - Algebraic Geometry
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 09/2017, Volume 115, Issue 3, pp. 638 - 692
To classify planar complex rational cuspidal curves E⊆P2 it remains to classify the ones with complement of log general type, that is, the ones for which... 
14H50 (primary) | 14J17 | 14R25 (secondary) | MATHEMATICS | Q-HOMOLOGY PLANES | Mathematics - Algebraic Geometry
Journal Article
Journal of algebra, ISSN 0021-8693, 06/2016, Volume 456, p. 207
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1016/j.jalgebra.2016.03.001 A... 
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 08/2012, Volume 258, Issue 2, pp. 421 - 457
A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We classify singular Q-homology planes that are C-1- or C*-ruled. We... 
ℚ-Homology plane | Homology plane | Acyclic surface | MATHEMATICS | WEIGHTED GRAPHS | homology plane | Q-homology plane | AFFINE LINES | acyclic surface | QUOTIENT SINGULARITIES | SURFACES
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2011, Volume 61, Issue 2, pp. 745 - 774
We consider singular Q-acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth... 
Exceptional ℚ-homology plane | Homology plane | Acyclic surface | MATHEMATICS | exceptional Q-homology plane | homology plane | AFFINE LINES | QUOTIENT SINGULARITIES | SURFACES | Mathematics - Algebraic Geometry
Journal Article
02/2012
Let E be a plane rational curve defined over complex numbers which has only locally irreducible singularities. The Coolidge-Nagata conjecture states that E is... 
Journal Article
Osaka J. Math, 2013, Volume 50, Issue no. 1, pp. 61 - 114
We show that if a normal \mathbb{Q}-acyclic complex surface has negative Kodaira dimension then its smooth locus is not of general type. This generalizes an... 
14J26 | 14P05 | 14J17
Journal Article
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