Premium
Gorenstein stable surfaces with K X 2 = 1 and p g > 0
Author(s) -
Franciosi Marco,
Pardini Rita,
Rollenske Sönke
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.201600090
Subject(s) - moduli space , mathematics , stratification (seeds) , pure mathematics , intersection (aeronautics) , genus , simple (philosophy) , moduli , surface (topology) , space (punctuation) , mathematical analysis , geometry , computer science , seed dormancy , philosophy , botany , germination , physics , epistemology , quantum mechanics , dormancy , engineering , biology , aerospace engineering , operating system
In this paper we consider Gorenstein stable surfaces withK X 2 = 1 and positive geometric genus. Extending classical results, we show that such surfaces admit a simple description as weighted complete intersection. We exhibit a wealth of surfaces of all possible Kodaira dimensions that occur as normalisations of Gorenstein stable surfaces withK X 2 = 1 ; forp g = 2 this leads to a rough stratification of the moduli space. Explicit non‐Gorenstein examples show that we need further techniques to understand all possible degenerations.