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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
Inventiones mathematicae, ISSN 0020-9910, 6/2014, Volume 196, Issue 3, pp. 733 - 771
Invent. Math. 196 (2014), no. 3, 733-771 In this paper we study holomorphic immersions of open Riemann surfaces into C^n whose derivative lies in a conical... 
32E10 | 32E30 | 49Q05 | 14Q05 | Mathematics, general | Mathematics | 14H50 | 32H02 | 32Q28 | MATHEMATICS | OKA PRINCIPLE | COMPLEX | CONJECTURES | SECTIONS | MANIFOLDS | COMPLETE MINIMAL-SURFACES | Riemann surfaces | Immersion
Journal Article
International journal of pure and applied mathematics : IJPAM, ISSN 1311-8080, 2012, Volume 78, Issue 2, pp. 193 - 195
Journal Article
The Michigan mathematical journal, ISSN 0026-2285, 07/2011, Volume 60, Issue 2, pp. 243 - 269
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 10/2018, Volume 24, Issue 2, pp. 483 - 506
Recently we have shown that the distance trisector curve is a transcendental curve. Since from the computational point of view this implies that no closed... 
Mathematics, general | Mathematics | Secondary 14H50 | Primary 51M05 | 68U05 | 65D18
Journal Article
Resultate der Mathematik, ISSN 1420-9012, 2019, Volume 74, Issue 3, pp. 1 - 24
We describe the effect of ramified morphisms on Harbourne constants of reduced effective divisors. With this goal, we introduce the pullback of a weighted... 
14J26 | algebraic surfaces | blowups | 14C20 | Mathematics, general | Mathematics | Algebraic curves | 14H50 | clusters of points | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 1/2018, Volume 110, Issue 1, pp. 35 - 43
We study the Clifford index c of a smooth irreducible curve X in the linear series |2H| on a special K3 surface S of degree 2n in $${{\mathbb P}}^{n+1}$$ P n +... 
Mathematics, general | Secondary 14H51 | Mathematics | Clifford index | K3 surfaces | Primary 14H50 | MATHEMATICS
Journal Article
Advances in Geometry, ISSN 1615-715X, 10/2019, Volume 19, Issue 4, pp. 555 - 572
To study the splitting of nodal plane curves with respect to contact conics, we define the of such curves and show that it can be used as an invariant to... 
Zariski pair | double cover | Splitting curve | 32S50 | 14E20 | 14H50 | 57N35 | PLANE QUARTICS | MATHEMATICS | Splitting | Conics | Topology | Curves
Journal Article
Manuscripta mathematica, ISSN 0025-2611, 07/2017, Volume 153, Issue 3-4, pp. 535 - 543
Let X be a smooth projective surface with Picard number 1. Let L be the ample generator of the N,ron-Severi group of X. Given an integer , we prove lower... 
Primary 14C20 | Secondary 14H50 | MATHEMATICS | ALGEBRAIC-SURFACES | P-2 | POINT | AMPLE DIVISORS
Journal Article
The Michigan mathematical journal, ISSN 0026-2285, 03/2015, Volume 64, Issue 1, pp. 155 - 168
For the completion B of a local geometric normal domain, V. Srinivas asked which subgroups of Cl B arise as the image of the map Cl A -> CI B on class groups... 
MATHEMATICS | SINGULARITIES | COMPLETIONS | CURVES | 14B07 | 14H50 | 14H10
Journal Article
Forum mathematicum, ISSN 1435-5337, 2020, Volume 32, Issue 1, pp. 63 - 78
We study locally Cohen–Macaulay curves of low degree in the Segre threefold and investigate the irreducible and connected components, respectively, of the... 
Locally Cohen–Macaulay curve | moduli space | Hilbert scheme | 14Q05 | pure sheaf | 14H50 | 14C05 | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | Locally Cohen-Macaulay curve | FAMILIES | MODULI
Journal Article
Mathematische Zeitschrift, ISSN 1432-1823, 2015, Volume 282, Issue 3-4, pp. 1017 - 1031
We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in... 
Tropical geometry | Mathematics, general | Tropical curves | Mathematics | 14H51 | 14H50 | Plane quartics | 14T05 | 14H45 | Algebraic geometry | MATHEMATICS | RIEMANN-ROCH | GEOMETRY
Journal Article
Mathematische Annalen, ISSN 0025-5831, 10/2016, Volume 366, Issue 1, pp. 219 - 247
The behavior of norms of roots of univariate trinomials $$z^{s+t} + p z^t + q \in \mathbb {C}[z]$$ z s + t + p z t + q ∈ C [ z ] for fixed support $$A =... 
55P15 | 55R10 | 12D10 | Mathematics, general | Mathematics | 14H50 | 14D05 | MATHEMATICS | STABLE POLYNOMIALS | AMEBAS | DETERMINANTS | GEOMETRY
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 04/2016, Volume 289, Issue 5-6, pp. 523 - 536
We classify globally generated vector bundles on P1×P2 with small first Chern class, i.e. c1=(a,b), a+b≤3. Our main method is to investigate the associated... 
curves in projective spaces | globally generated | vector bundles | 14J60 | 14M07 | 14H50 | Segre variety | Vector bundles | Curves in projective spaces | Globally generated | MATHEMATICS | CURVES
Journal Article
Boletim da Sociedade Brasileira de Matemática, ISSN 1678-7714, 2018, Volume 50, Issue 3, pp. 717 - 743
Let C be a nodal curve and L be an invertible sheaf on C. Let $$\alpha _{L}:C\dashrightarrow J_{C}$$ α L : C ⤏ J C be the degree-1 rational Abel map, which... 
Mathematics, general | Nodal curves | Mathematics | 14H50 | Theoretical, Mathematical and Computational Physics | Abel map | MATHEMATICS | COMPACTIFICATION | Mathematics - Algebraic Geometry
Journal Article
manuscripta mathematica, ISSN 0025-2611, 5/2018, Volume 156, Issue 1, pp. 137 - 147
In this note we compute the number of general points through which a general Brill–Noether space curve passes. 
Geometry | Topological Groups, Lie Groups | 14H60 | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 14H50 | MATHEMATICS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 10/2013, Volume 286, Issue 14-15, pp. 1407 - 1423
One classifies the globally generated vector bundles on Pn with the first Chern class c1 = 3. The case c1 = 1 is very easy, the case c1 = 2 was done in [42],... 
Secondary: 14H50, 14N25 | Primary: 14J60 | vector bundle | globally generated sheaf | Projective space | Vector bundle | Globally generated sheaf
Journal Article
Advances in Geometry, ISSN 1615-715X, 10/2016, Volume 16, Issue 4, pp. 437 - 464
Given a point (the light position) in ℙ and an algebraic surface 𝓩 (the mirror) of ℙ , the caustic by reflection Σ 𝓩. We use the ramification method to... 
polar | 14N10 | pro-branch | 14H50 | 14N05 | Caustic | 14E05 | class | intersection number | MATHEMATICS | FOCAL LOCI | Hazardous substances
Journal Article
Advances in mathematics (New York. 1965), 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
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