Zariski surfaces

Piotr Blass

GDML_Books, (1983), p.

Résumé

CONTENTSAcknowledgements...................................................................................................5Introduction..............................................................................................................6Notations..................................................................................................................8Chapter I. Zariski surfaces: definition and general properties................................10Chapter II. The theory of adjoints..........................................................................14  Introduction..........................................................................................................14  §1. Behaviour of $ω_X$ under restriction to open subschemes............................15  §2. Behaviour of $ω_X$ under certain birational maps..........................................16  §3. Affine case, adjoints........................................................................................16  §4. Projective case................................................................................................20  §5. Theory of l-adjoints for l ≥ 1 (an outline).........................................................24  §6. Valuation theory for differentials.....................................................................25Chapter III. An example relating to a question of O. Zariski...................................28  Introduction..........................................................................................................28  Part 1. Equation of the surface, singularities in characteristic 2..........................29  Part 2. .................................................................................................................33  Part 3. The singularity of F̅ at infinity....................................................................44    §1. Introductory remarks...................................................................................45    §2. Resolution of the singularity at infinity.........................................................47    §3. Behaviour of differentials at infinity under the resolution.............................52  Part 4. Conclusion................................................................................................57  Part 5. Appendix...................................................................................................58Chapter IV. Generic Zariski surfaces..........................................................................64Chapter V. Richness of the class of Zariski surfaces.................................................76References................................................................................................................80

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