Equations defining reducible Kummer surfaces in ℙ⁵
Annales Polonici Mathematici (1996)
- Volume: 63, Issue: 1, page 51-62
- ISSN: 0066-2216
Access Full Article
top
Abstract
topHow to cite
topTomasz Szemberg. "Equations defining reducible Kummer surfaces in ℙ⁵." Annales Polonici Mathematici 63.1 (1996): 51-62. <http://eudml.org/doc/262777>.
@article{TomaszSzemberg1996,
abstract = {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.},
author = {Tomasz Szemberg},
journal = {Annales Polonici Mathematici},
keywords = {Kummer surfaces; intersections of quadrics; Kummer surface; product of elliptic curves; Jacobians of stable reducible curves},
language = {eng},
number = {1},
pages = {51-62},
title = {Equations defining reducible Kummer surfaces in ℙ⁵},
url = {http://eudml.org/doc/262777},
volume = {63},
year = {1996},
}
TY - JOUR
AU - Tomasz Szemberg
TI - Equations defining reducible Kummer surfaces in ℙ⁵
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 1
SP - 51
EP - 62
AB - 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.
LA - eng
KW - Kummer surfaces; intersections of quadrics; Kummer surface; product of elliptic curves; Jacobians of stable reducible curves
UR - http://eudml.org/doc/262777
ER -
References
top- [AvM1] M. Adler and P. van Moerbeke, Geodesic flow on SO(4) and intersection of quadrics, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), 4613-4616. Zbl0545.58027
- [AvM2] M. Adler and P. van Moerbeke, The intersection of four quadrics in ℙ⁶, abelian surfaces and their moduli, Math. Ann. 279 (1987), 25-85. Zbl0607.14030
- [B] W. Barth, Affine parts of abelian surfaces as complete intersections of four quadrics, Math. Ann. 278 (1987), 117-131. Zbl0675.14023
- [BPV] W. Barth, C. Peters and A. van de Ven, Compact Complex Surfaces, Springer, Berlin, 1984. Zbl0718.14023
- [Ba] Th. Bauer, Projective images of Kummer surfaces, Math. Ann. 299 (1994), 155-170. Zbl0793.14029
- [LB] H. Lange and Ch. Birkenhake, Complex Abelian Varieties, Grundlehren Math. Wiss. 302, Springer, New York, 1992.
- [M] D. Mumford, On the equations defining abelian varieties. I, Invent. Math. 1 (1966), 287-354. Zbl0219.14024
- [S1] T. Szemberg, A 4₃ configuration of lines and conics in ℙ⁵, Ann. Polon. Math. 60 (1995), 145-158.
- [S2] T. Szemberg, Intersections of quadrics in ℙ⁵, Kummer surfaces and their moduli, thesis, Erlangen, 1994.
- [S-D] B. Saint-Donat, Projective models of K3 surfaces, Amer. J. Math. 96 (1974), 602-639. Zbl0301.14011
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.