A 4₃ configuration of lines and conics in ℙ⁵
Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.
Equations defining reducible Kummer surfaces in ℙ⁵
Principally polarized abelian surfaces are the Jacobians of smooth genus 2 curves or of stable genus 2 curves of special type. In [S] we studied equations describing Kummer surfaces in the case of an irreducible principal polarization on the abelian surface. The aim of this note is to give a treatment of the second case. We describe intermediate Kummer surfaces coming from abelian surfaces carrying a product principal polarization. In Proposition 12 we give explicit equations of these surfaces in...
Automorphisms of Riemann surfaces with two fixed points
We give an upper bound for the order of an automorphism of a Riemann surface with two fixed points. The main results are presented in Theorems 1.4 and 2.4.
Double covers and Calabi-Yau varieties
Geometry of the locus of polynomials of degree 4 with iterative roots
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
Remarks on the Nagata Conjecture
2000 Mathematics Subject Classification: 14C20, 14E25, 14J26. The famous Nagata Conjecture predicts the lowest degree of a plane curve passing with prescribed multiplicities through given points in general position. We explain how this conjecture extends naturally via multiple point Seshadri constants to ample line bundles on arbitrary surfaces. We show that if there exist curves of unpredictable low degree, then they must have equal multiplicities in all but possibly one of the given...
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