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Classification and syzygies of smooth projective varieties with 2‐regular structure sheaf

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  • Sijong Kwak
  • Jinhyung Park

Abstract

The geometric and algebraic properties of smooth projective varieties with 1‐regular structure sheaf are well understood, and the complete classification of these varieties is a classical result. The aim of this paper is to study the next case: smooth projective varieties with 2‐regular structure sheaf. First, we give a classification of such varieties using adjunction mappings. Next, under suitable conditions, we study the syzygies of section rings of those varieties to understand the structure of the Betti tables, and show a sharp bound for Castelnuovo–Mumford regularity.

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  • Sijong Kwak & Jinhyung Park, 2020. "Classification and syzygies of smooth projective varieties with 2‐regular structure sheaf," Mathematische Nachrichten, Wiley Blackwell, vol. 293(7), pages 1378-1389, July.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:7:p:1378-1389
    DOI: 10.1002/mana.201900345
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