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Virtual complete intersections in \(\mathbb{P}^1\times\mathbb{P}^1\). (English) Zbl 1441.13031
Summary: The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces \(\mathbb{P}^1\times\mathbb{P}^1\), we investigate which sets of points have a virtual resolution that is a Koszul complex on a regular sequence. This paper provides conditions on sets of points; some of which guarantee the points have this property, and some of which guarantee the points do not have this property.
13D02 Syzygies, resolutions, complexes and commutative rings
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
Full Text: DOI
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