Divisors on K3 surfaces and Hilbert schemes

by Jonas Baltes
Doctoral thesis
Date of Examination:2024-04-29
Date of issue:2024-06-27
Advisor:Prof. Dr. Frank Gounelas
Referee:Prof. Dr. Frank Gounelas
Referee:Prof. Dr. Viktor Pidstrygach
Referee:Prof. Dr. Matthias Schütt
Persistent Address: http://dx.doi.org/10.53846/goediss-10575

 

 

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Abstract

English

This thesis consists of three chapters. In the first chapter we study rational curves on K3 surfaces and show that on elliptic K3s there are rational curves whose arithmetic genus tends to infinity. In the second chapter we study divisors on Hyperkähler varieties and how their birational behaviour is determined by the surrounding variety. In the final chapter with the previous concepts we study curves on surfaces and relate the singularities of such curves to certain divisors and curves on Hilbert schemes, giving a link between Hilbert schemes and Seshadri constants.
Keywords: K3 surface; Hyperkähler; Seshadri constant; Nagata conjecture; Rational curves; Lefschetz theorem
 
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