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Classification and syzygies of smooth projective varieties with 2‐regular structure sheaf
Author(s) -
Kwak Sijong,
Park Jinhyung
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900345
Subject(s) - mathematics , adjunction , sheaf , pure mathematics , section (typography) , betti number , algebraic variety , projective test , algebraic number , algebra over a field , mathematical analysis , advertising , business
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.