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SUMMARY:Fibrations in (1\,2)-Surfaces
DTSTART:20240403T123000Z
DTEND:20240403T133000Z
DTSTAMP:20240530T150600Z
UID:indico-event-264@events.dm.unipi.it
DESCRIPTION:Speakers: Roberto Pignatelli (Trento)\n\nThe content of this s
eminar stems from an ongoing collaboration with S. Coughlan\, Y. Hu\, and
T. Zhang. By "(1\,2)-surfaces" we denote complex algebraic surfaces with c
anonical singularities\, ample canonical system\, volume 1\, and geometric
genus 2. This is a class of surfaces that played a significant role in th
e theory of surfaces of general type in the last century and has shown in
this century to also play an important role in the theory of 3-dimensional
varieties\, particularly in the recent proof of the 3-dimensional Noether
inequality obtained by J. Chen\, M. Chen\, and C. Jiang. In fact\, 3-dime
nsional varieties fibred in surfaces of type (1\,2) play a role in this p
roof similar to that played by fibrations in curves of genus 2 in lower di
mensions. In this seminar\, I will introduce the concept of "simple" fibra
tion in surfaces of type (1\,2) and explain how through this concept we ob
tained a complete classification of 3-folds that satisfy the equality i
n the aforementioned inequality. I will also discuss analogies and differe
nces with the 2-dimensional case. Finally\, I will mention some open probl
ems that we are currently investigating.\n\nhttps://events.dm.unipi.it/eve
nt/264/
LOCATION:Aula Seminari (Department of Mathematics)
URL:https://events.dm.unipi.it/event/264/
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