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arXiv · 1604.06228

A note on homogeneous ideals of polarized abelian surfaces

Daniele Agostini
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Abstract

Gross and Popescu conjectured that the homogeneous ideal of an embedded $(1,d)$-polarized abelian surface is generated by quadrics and cubics for $d\geq 9$. We prove this using the projective normality of the embedding. It follows that the homogeneous ideal of an abelian surface embedded by a complete linear system is generated by quadrics and cubics, with three exceptions.

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Daniele Agostini. 2016-04-21. A note on homogeneous ideals of polarized abelian surfaces. https://doi.org/10.1112/blms.12027

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