Search results for "Endomorphism"

showing 2 items of 12 documents

Humbert surfaces and the Kummer plane

2003

A Humbert surface is a hypersurface of the moduli space A 2 \mathcal A_2 of principally polarized abelian surfaces defined by an equation of the form a z 1 + b z 2 + c z 3 + d ( z 2 2 − z 1 z 3 ) + e = 0 az_1+bz_2+cz_3+d(z_2^2-z_1z_3)+e=0 with integers a , … , e a,\ldots ,e . We give geometric characterizations of such Humbert surfaces in terms of the presence of certain curves on the associated Kummer plane. Intriguingly this shows that a certain plane configuration of lines and curves already carries all information about principally polarized abelian surfaces admitting a symmetric endomorphism with given discriminant.

Surface (mathematics)Pure mathematicsEndomorphismHypersurfacePlane (geometry)Applied MathematicsGeneral MathematicsMathematical analysisAlgebraic geometryAbelian groupComplex numberModuli spaceMathematicsTransactions of the American Mathematical Society
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Bifurcations in the elementary Desboves family

2017

International audience; We give an example of a family of endomorphisms of $\mathbb{P}^2(\mathbb{C})$ whose Julia set depends continuously on the parameter and whose bifurcation locus has non-empty interior.

[ MATH ] Mathematics [math]Pure mathematicsEndomorphismMathematics - Complex VariablesApplied MathematicsGeneral Mathematics010102 general mathematicsDynamical Systems (math.DS)MSC: 32H50 37F4516. Peace & justice01 natural sciencesJulia setDynamicsRational mapsBifurcation locus0103 physical sciencesFOS: Mathematics32H50 37F45 37F50010307 mathematical physics0101 mathematics[MATH]Mathematics [math]Complex Variables (math.CV)Mathematics - Dynamical SystemsMathematics
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