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ICRA 2018-Workshop Prague- 7-13 August 2018
Three Lectures on quiver Grassmannians
Giovanni Cerulli Irelli
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08/08/18 Giovanni Cerulli Irelli
Info
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08/08/18 Giovanni Cerulli Irelli
Plan
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ICRA 2018-Workshop Prague- 7-13 August 2018
Generalities on quiver Grassmannians
Giovanni Cerulli Irelli
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Quiver representations
08/08/18 Giovanni Cerulli Irelli
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Quiver Representations
08/08/18 Giovanni Cerulli Irelli
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Dynkin and affine quivers
08/08/18 Giovanni Cerulli Irelli
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Representation varieties
08/08/18 Giovanni Cerulli Irelli
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Degeneration order for Dynkin quivers
08/08/18 Giovanni Cerulli Irelli
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Ringel map
08/08/18 Giovanni Cerulli Irelli
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Ringel-Euler form
08/08/18 Giovanni Cerulli Irelli
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Quiver Grassmannian (set theoretic definition)
08/08/18 Giovanni Cerulli Irelli
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Example 0: the Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Example 0: the Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Example 0: the Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Example 0: the Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Example 0: the Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Example 0: the Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Example 0: the Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Example 1: The flag variety
08/08/18 Giovanni Cerulli Irelli
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Example 2
08/08/18 Giovanni Cerulli Irelli
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Example 3
08/08/18 Giovanni Cerulli Irelli
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Example 4
08/08/18 Giovanni Cerulli Irelli
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Example 5
08/08/18 Giovanni Cerulli Irelli
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Example 6
08/08/18 Giovanni Cerulli Irelli
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Example 6
08/08/18 Giovanni Cerulli Irelli
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Example 6
08/08/18 Giovanni Cerulli Irelli
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A result of Reineke
08/08/18 Giovanni Cerulli Irelli
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Strengthening by Ringel
08/08/18 Giovanni Cerulli Irelli
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What is a subrepresentation?
08/08/18 Giovanni Cerulli Irelli
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First realization: universal quiver Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Universal quiver Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Quiver Grassmannian: scheme-theoretic definition
08/08/18 Giovanni Cerulli Irelli
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Universal quiver Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Universal quiver Grassmannian
08/08/18 Giovanni Cerulli Irelli
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Dimension estimate for quiver Grassmannians
08/08/18 Giovanni Cerulli Irelli
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Quiver Grassmannians associated with rigid reps
08/08/18 Giovanni Cerulli Irelli
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Non-emptyness of “rigid” quiver Grassmannians
08/08/18 Giovanni Cerulli Irelli
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Criterion of non-emptyness by Reineke-Kerkman
08/08/18 Giovanni Cerulli Irelli
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2) Quiver Grassmannians as geometric quotients
08/08/18 Giovanni Cerulli Irelli
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Hom0 (e,M)
08/08/18 Giovanni Cerulli Irelli
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Hom(e,M) is Ge-invariant
08/08/18 Giovanni Cerulli Irelli
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Ge acts freely on Hom0(e,M)
08/08/18 Giovanni Cerulli Irelli
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Quotient map
08/08/18 Giovanni Cerulli Irelli
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Quiver Grassmannians as geometric quotients
08/08/18 Giovanni Cerulli Irelli
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Tangent space formula
08/08/18 Giovanni Cerulli Irelli
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Isostrata
08/08/18 Giovanni Cerulli Irelli
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Properties of isostrata
08/08/18 Giovanni Cerulli Irelli
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Generic subrepresentation types
08/08/18 Giovanni Cerulli Irelli
