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Godeaux, Campedelli, and surfaces of general type with χ = 4 and 2 ≤ K 2 ≤ 8
Author(s) -
Iqbal Sohail
Publication year - 2017
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.201500445
Subject(s) - mathematics , stack (abstract data type) , type (biology) , surface (topology) , construct (python library) , pure mathematics , moduli , connected component , component (thermodynamics) , minimal surface , geometry , combinatorics , computer science , ecology , physics , quantum mechanics , biology , programming language , thermodynamics
We construct simply connected surfaces of general type with invariants χ ( O ) = 4 and 2 ≤ K 2 ≤ 8 . We use Q ‐Gorenstein deformations in conjunction with explicit constructions that express the canonical rings by generators and relations. The canonical rings of the surfaces are described as projections. The whole construction is simplified by the use of key varieties based on Steiner 3‐folds. As a consequence of the construction we find two families, each family in a different connected component of the moduli stackM ¯ 2 , 1 , and each linking a Campedelli surface with a Godeaux surface.