Correspondence Scrolls

Abstract

This paper initiates the study of a class of schemes that we call correspondence scrolls, which includes the rational normal scrolls and linearly embedded projective bundle of decomposable bundles, as well as degenerate K3 surfaces, Calabi-Yau threefolds, and many other examples.

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Acknowledgements

The first author was partially supported by NSF grant No. 1502190. He would like to thank Frank-Olaf Schreyer, who pointed out in their joint work that the K3 carpets could be regarded as coming from correspondences. The second author was supported by NSF grant No. 1440140 while he was a Postdoctoral Fellow at the Mathematical Sciences Research Institute in Berkeley, CA. He would like to thank Aldo Conca and Matteo Varbaro for some helpful comments.

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Correspondence to David Eisenbud.

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Eisenbud, D., Sammartano, A. Correspondence Scrolls. Acta Math Vietnam 44, 101–116 (2019). https://doi.org/10.1007/s40306-018-0296-6

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Keywords

  • Rational normal scroll
  • Veronese embedding
  • Join variety
  • Multiprojective space
  • Variety of complexes
  • Variety of minimal degree
  • Double structure
  • K3 surface
  • Calabi-Yau scheme
  • Gorenstein ring
  • Gröbner basis

Mathematics Subject Classification (2010)

  • Primary 14J40
  • Secondary 13H10
  • 13C40
  • 13P10
  • 14J26
  • 14J28
  • 14J32
  • 14M05
  • 14M12
  • 14M20