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Automorphisms of Riemann surfaces with two fixed points

100%
Szemberg T.
Annales Polonici Mathematici
|
1991
|
tom 55
|
nr 1
343-347
EN
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.
2
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Equations defining reducible Kummer surfaces in ℙ⁵

100%
Szemberg T.
Annales Polonici Mathematici
|
1996
|
tom 63
|
nr 1
51-62
EN
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 ℙ⁵.
3
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A 4₃ configuration of lines and conics in ℙ⁵

100%
Szemberg T.
Annales Polonici Mathematici
|
1994-1995
|
tom 60
|
nr 2
145-158
EN
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.
4
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Geometry of the locus of polynomials of degree 4 with iterative roots

64%
Strycharz-Szemberg B., Szemberg T.
Open Mathematics
|
2011
|
tom 9
|
nr 2
338-345
EN
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
5
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Double covers and Calabi-Yau varieties

64%
Cynk S., Szemberg T.
Banach Center Publications
|
1998
|
tom 44
|
nr 1
93-101
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