Seshadri constants and geometry of surfaces [Elektronische Ressource] / von Wioletta Syzdek

Description

Seshadri constantsand geometry of surfacesDissertationzur Erlangung des GradesDoktor der Naturwissenschaften(Dr. rer. nat.)vorgelegt beimFachbereich Mathematik und Informatikder Universit¨at Duisburg-Essenvon Wioletta Syzdekaus My´sleniceTag der Disputation 20. Juli 2005Vorsitzender der Prufungsk¨ ommission Prof. Dr. Karl-Josef WitschErster Gutachter Prof. Dr. Tomasz SzembergZweiter Gutachter Prof. Dr. Eckart ViehwegAcknowledgmentsI am very grateful to Tomasz Szemberg for his invaluable support and theguidance throughout the preparation of this thesis.IwanttothankmyformerteacherHalszkaTutaj-Gasinsk´ aforthepossibilityofbeginningofmyPhDstudiesandforlettingmeknowtheideaofsymplecticpacking.I would like to thank H´el`ene Esnault and Eckart Viehweg for making mystudy in Essen possible, for help with bureaucracy - in particular withAusl¨anderamt in Essen.I want to thank my colleagues: Kay Rulling¨ , Stefan Kukulies and AndreChatzistamatiou for friendly atmosphere in the office and help during mystudy here.Finally I would like to thank my parents, my grandmother and my brotherfor support in difficult times.Contents1 Introduction 12 Seshadri constants and the Nagata-Biran conjecture. 32.1 Seshadri constants - basics definitions and properties. . . . . . 32.2 Multiple points Seshadri constants and the Nagata-Biran con-jecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Seshadri constants on ruled surfaces. 93.

Sujets

• Mathematics

Informations

• Publié par: universitat_duisburg-essen
• Publié le: 01 janvier 2005
• Nombre de lectures: 15
• Langue: English

Extrait

Seshadri constants and geometry of surfaces

Dissertation zur Erlangung des Grades Doktor der Naturwissenschaften (Dr. rer. nat.)

vorgelegt beim Fachbereich Mathematik und Informatik derUniversita¨tDuisburg-Essen

Tag der Disputation

von Wioletta Syzdek ausMys´lenice

20. Juli 2005

VorsitzenderderPr¨ufungskommissionProf.Dr.Karl-JosefWitsch Erster Gutachter Prof. Dr. Tomasz Szemberg Zweiter Gutachter Prof. Dr. Eckart Viehweg

Acknowledgments

I am very grateful to Tomasz Szemberg for his invaluable support and the guidance throughout the preparation of this thesis.

IwanttothankmyformerteacherHalszkaTutaj-Gasin´skaforthepossibility of beginning of my PhD studies and for letting me know the idea of symplectic packing.

IwouldliketothankHe´le`neEsnaultandEckartViehwegformakingmy study in Essen possible, for help with bureaucracy - in particular with Ausl¨anderamtinEssen.

Iwanttothankmycolleagues:KayRu¨lling,StefanKukuliesandAndre Chatzistamatiou for friendly atmosphere in the office and help during my study here.

Finally I would like to thank my parents, my grandmother and my brother for support in difficult times.

Contents 1 Introduction 1 2 Seshadri constants and the Nagata-Biran conjecture. 3 2.1 Seshadri constants - basics definitions and properties. . . . . . 3 2.2 Multiple points Seshadri constants and the Nagata-Biran con- jecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Seshadri constants on ruled surfaces. 9 3.1 Ruled surfaces - basic definitions and properties. . . . . . . . . 9 3.2 Linear systems on ruled surfaces. . . . . . . . . . . . . . . . . 12 3.3 Elementary transformation of a ruled surface. . . . . . . . . . 12 3.4 Seshadri Constants on ruled surfaces. . . . . . . . . . . . . . . 19 4 Seshadri fibrations. 23 5 R-R expected curves, Nagata-Biran conjecture and symplec- tic packing. 31 5.1 Nagata submaximal curves onP 1 ×P 1 . . 31 . . . . . . . . . . . . 5.2 Symplectic packing and the Nagata-Biran conjecture. . . . . . 33 5.3 Application in the problem of symplectic packing ofP 1 ×P 1 . . 60 5.4 Conjecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 References 61