Quasi-homogeneous linear systems on ℙ² with base points of multiplicity 7, 8, 9, 10

Marcin Dumnicki

Displaying similar documents to “Quasi-homogeneous linear systems on ℙ² with base points of multiplicity 7, 8, 9, 10”

Pencils of irreducible rational curves and plane Jacobian conjecture

Nguyen Van Chau (2011)

Annales Polonici Mathematici

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In certain cases the invertibility of a polynomial map F = (P,Q): ℂ²→ ℂ² can be characterized by the irreducibility and the rationality of the curves aP+bQ = 0, (a:b) ∈ ℙ¹.

Nagata submaximal curves on ℙ¹ × ℙ¹

Wioletta Syzdek (2003)

Annales Polonici Mathematici

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The aim of this paper is to show that on ℙ¹ × ℙ¹ with a polarization of type (2,1) there are no R-R expected submaximal curves through any 10 ≤ r ≤ 15 points.

Cutting diagram method for systems of plane curves with base points

Marcin Dumnicki (2007)

Annales Polonici Mathematici

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We develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne conjecture holds for systems with base points of equal multiplicity bounded by 42.

A polynomial class of Markus-Yamabe counterexamples.

Anna Cima, Armengol Gasull, Francesc Mañosas (1997)

Publicacions Matemàtiques

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In the paper [CEGHM] a polynomial counterexample to the Markus-Yamabe Conjecture and to the discrete Markus-Yamabe Question in dimension n ≥ 3 are given. In the present paper we explain a way for obtaining a family of polynomial counterexamples containing the above ones. Finally we study the global dynamics of the examples given in [CEGHM].

Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three.

H. Hofer (1993)

Inventiones mathematicae

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Average distributions and products of special values of L-series

Amir Akbary, Chantal David, Robert Juricevic (2004)

Acta Arithmetica

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Algorithms for finding good examples for the $a b c$ and Szpiro conjectures.

Nitaj, Abderrahmane (1993)

Experimental Mathematics

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On nodal plane curves.

Z. Ran (1986)

Inventiones mathematicae

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Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves

Min Sha, Igor E. Shparlinski (2015)

Acta Arithmetica

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We obtain new results concerning the Lang-Trotter conjectures on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In particular, we improve a result of A. C. Cojocaru and the second author (2008) towards the Lang-Trotter conjecture on average for polynomially parameterised families of elliptic curves when the parameter runs through a set of rational numbers of...