Zariski surfaces

Piotr Blass

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1983

Abstract

top
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

How to cite

top

Piotr Blass. Zariski surfaces. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1983. <http://eudml.org/doc/268513>.

@book{PiotrBlass1983,
abstract = {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},
author = {Piotr Blass},
keywords = {characteristic p; rationality of Zariski surfaces; generic Zariski surface; rank of Neron-Severi group; adjoints; multiadjoints; genus},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Zariski surfaces},
url = {http://eudml.org/doc/268513},
year = {1983},
}

TY - BOOK
AU - Piotr Blass
TI - Zariski surfaces
PY - 1983
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
KW - characteristic p; rationality of Zariski surfaces; generic Zariski surface; rank of Neron-Severi group; adjoints; multiadjoints; genus
UR - http://eudml.org/doc/268513
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.