Lang’s conjecture in characteristic : an explicit bound
Alexandru Buium, José Felipe Voloch (1996)
Compositio Mathematica
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Alexandru Buium, José Felipe Voloch (1996)
Compositio Mathematica
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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.
Nguyen Van Chau (2012)
Annales Polonici Mathematici
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It is shown that every polynomial function P:ℂ² → ℂ with irreducible fibres of the same genus must be a coordinate. Consequently, there do not exist counterexamples F = (P,Q) to the Jacobian conjecture such that all fibres of P are irreducible curves with the same genus.
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.
David Eisenbud, Joe Harris (1992)
Compositio Mathematica
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Serge Lang (1960)
Publications Mathématiques de l'IHÉS
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Marco Andreatta, Elena Chierici, Gianluca Occhetta (2004)
Open Mathematics
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Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension...
Poonen, Bjorn, Stoll, Michael (1999)
Annals of Mathematics. Second Series
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Yu I. Manin (1993)
Compositio Mathematica
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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...
Nitaj, Abderrahmane (1993)
Experimental Mathematics
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D. Gieseker (1982)
Inventiones mathematicae
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Dan Abramovich, Joe Harris (1991)
Compositio Mathematica
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