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Seminario del 2018
2018
16 marzo
The history of philosophy is full of deep and unanswered
questions. Who are we? What is our purpose in this world? How many
QQ-Fano threefolds exist in high codimension?
Prophets Mori and Mukai in the late 80s provided a classification of
smooth Fano threefolds of index one, and their 17+88 families are an
irreplaceable tool in every birational geometer working kit.
More important than the list itself was the strategy (the 'vector
bundle method') and the mantra: Fano threefolds arise as linear
section of "good" varieties coming from representation theory.
The same results sadly does not extends to the QQ-Fano threefolds case
(the natural playground for MMPers). Tom and Jerry models provides a
good level of understanding up to codimension three, but the garden is
still wild and untamed. In this talk we will provide an overview of
the subject, and we will report on some recent progress in the
classification.