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Equations and Syzygies of K3 Carpets and Unions of Scrolls

  • David EisenbudEmail author
  • Frank-Olaf Schreyer
Article

Abstract

We describe the equations and Gröbner bases of some degenerate K3 surfaces associated to rational normal scrolls. These K3 surfaces are members of a class of interesting singular projective varieties we call correspondence scrolls. The ideals of these surfaces are nested in a simple way that allows us to analyze them inductively. We describe explicit Gröbner bases and syzygies for these objects over the integers and this lets us treat them in all characteristics simultaneously.

Keywords

K3 surfaces Green’s conjecture in positive characteristic Canonical curves Canonical ribbons K3 carpets 

Mathematics Subject Classification (2010)

Primary 14H99; Secondary 13D02 14H51 

Notes

Funding Information

The study is partially supported by the National Science Foundation. This work is a contribution to Project I.6 of the second author within the SFB-TRR 195 “Symbolic Tools in Mathematics and their Application” of the German Research Foundation (DFG).

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA
  2. 2.Mathematical Sciences Research InstituteBerkeleyUSA
  3. 3.Fachbereich MathematikUniversität des SaarlandesSaarbrückenGermany

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