Abstract
A non-classical Godeaux surface is a minimal surface of general type with χ = K 2 = 1 but with h 01 0. We prove that such surfaces fulfill h 01 = 1 and they can exist only over fields of positive characteristic at most 5. Like non-classical Enriques surfaces they fall into two classes: the singular and the supersingular ones. We give a complete classification in characteristic 5 and compute their Hodge-, Hodge-Witt- and crystalline cohomology (including torsion). Finally, we give an example of a supersingular Godeaux surface in characteristic 5.
Original language | English |
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Pages (from-to) | 623-637 |
Number of pages | 15 |
Journal | Mathematische Annalen |
Volume | 343 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2009 |
Externally published | Yes |