Date:
Sun, 21/01/202411:00-13:00
Location:
Ross 70A
Zoom link
https://huji.zoom.us/j/82253214545?pwd=WEVHMmpEYmRFeW1qdnB1K3FXZFg3QT09
Meeting ID: 822 5321 4545
Passcode: 751126
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link for recordings:
https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=ac807267-3220-41fa-8d5c-b07d00890eba
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Seminar notes
https://sites.google.com/site/howardnuermath/notes
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Michael Temkin and Howard Nuer "Minimal model program" (course number 80832)
Description: The goal of this course is to provide an introduction to the minimal model
program which aims to study the birational geometry of varieties by constructing
for each birational equivalence class a representative which is minimal or
canonical in a certain sense.
It is a classical result that for non-rational surfaces there always exists a minimal smooth representative,
which can be constructed by first resolving singularities of an arbitrary representative, and then
successively blowing down exceptional curves. For rational surfaces, however,
this uniqueness fails, and the different minimal models are connected by so-called Sarkisov links.
Already the case of threefolds is tremendously more difficult -- one is forced to allow mildly
singular minimal models and in general there exist many different minimal models
connected by flops. In addition to blowing down divisors and flops, one also has to consider
much finer contractions, called flips, which only alter the geometry in codimension 2
but improve the effective cone of curves on the model, etc.
In this course we will give an introduction to these methods, along the lines of the book
of Kollár and Mori.
If time permits, we will also discuss some of the more recent great achievements:
1) The construction of canonical models by Hacon, McKernan and others.
2) The boundedness of Fano varieties by recent Fields medalist Birkar.
3) The homological minimal model program which seeks to understand birational
geometry through derived categories of sheaves and their semiorthogonal decompositions.
Prerequisites: a good knowledge of Hartshorne. That is, we do not ask anything beyond Hartshorne, but unlike usual courses based on Hartshorne, a reasonable familiarity with section 5 is assumed (for example, intersection form, blowing down exceptional curves).
https://huji.zoom.us/j/82253214545?pwd=WEVHMmpEYmRFeW1qdnB1K3FXZFg3QT09
Meeting ID: 822 5321 4545
Passcode: 751126
------------------------------------------------------------------------------------------------------
link for recordings:
https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=ac807267-3220-41fa-8d5c-b07d00890eba
----------------------------------------------------------------------------------------------------
Seminar notes
https://sites.google.com/site/howardnuermath/notes
---------------------------------------------------------------------------------------------
Michael Temkin and Howard Nuer "Minimal model program" (course number 80832)
Description: The goal of this course is to provide an introduction to the minimal model
program which aims to study the birational geometry of varieties by constructing
for each birational equivalence class a representative which is minimal or
canonical in a certain sense.
It is a classical result that for non-rational surfaces there always exists a minimal smooth representative,
which can be constructed by first resolving singularities of an arbitrary representative, and then
successively blowing down exceptional curves. For rational surfaces, however,
this uniqueness fails, and the different minimal models are connected by so-called Sarkisov links.
Already the case of threefolds is tremendously more difficult -- one is forced to allow mildly
singular minimal models and in general there exist many different minimal models
connected by flops. In addition to blowing down divisors and flops, one also has to consider
much finer contractions, called flips, which only alter the geometry in codimension 2
but improve the effective cone of curves on the model, etc.
In this course we will give an introduction to these methods, along the lines of the book
of Kollár and Mori.
If time permits, we will also discuss some of the more recent great achievements:
1) The construction of canonical models by Hacon, McKernan and others.
2) The boundedness of Fano varieties by recent Fields medalist Birkar.
3) The homological minimal model program which seeks to understand birational
geometry through derived categories of sheaves and their semiorthogonal decompositions.
Prerequisites: a good knowledge of Hartshorne. That is, we do not ask anything beyond Hartshorne, but unlike usual courses based on Hartshorne, a reasonable familiarity with section 5 is assumed (for example, intersection form, blowing down exceptional curves).