# Equations defining reducible Kummer surfaces in ℙ⁵

Annales Polonici Mathematici (1996)

- Volume: 63, Issue: 1, page 51-62
- ISSN: 0066-2216

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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

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- [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

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