Three Lectures on quiver Grassmanniansgiovanni.cerulliirelli/...ICRA 2018-Workshop Prague- 7-13 August 2018 Three Lectures on quiver Grassmannians Giovanni Cerulli Irelli

ICRA 2018-Workshop Prague- 7-13 August 2018

Three Lectures on quiver Grassmannians

Giovanni Cerulli Irelli

ICRA 2018-Workshop Prague- 7-13 August 2018

Cellular decomposition and property (S)

Giovanni Cerulli Irelli

Alfa-partitions

11/08/18 Giovanni Cerulli Irelli

Cellular decomposition

11/08/18 Giovanni Cerulli Irelli

Property (S)

11/08/18 Giovanni Cerulli Irelli

Property (S) does not imply cell dec

11/08/18 Giovanni Cerulli Irelli

Basic properties of cell dec and property (S)

11/08/18 Giovanni Cerulli Irelli

Springer fibers

11/08/18 Giovanni Cerulli Irelli

Properties (S) and (C) for quiver representations

11/08/18 Giovanni Cerulli Irelli

Main results

11/08/18 Giovanni Cerulli Irelli

Remarks on Theorem 3

11/08/18 Giovanni Cerulli Irelli

Remarks on Theorem 3

11/08/18 Giovanni Cerulli Irelli

Decomposition induced by Short exact Sequences

11/08/18 Giovanni Cerulli Irelli

The strata induced by a s.e.s.

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Image of the strata

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Proof of the Lemma

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A “nice” stratum in the image

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Generating S.E.S.

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Reduction Theorem

11/08/18 Giovanni Cerulli Irelli

Ringel reflections

11/08/18 Giovanni Cerulli Irelli

Ringel reflections

11/08/18 Giovanni Cerulli Irelli

Generalized almost split sequences

11/08/18 Giovanni Cerulli Irelli

Properties of Ringel reflections

11/08/18 Giovanni Cerulli Irelli

Main property of Ringel reflections

11/08/18 Giovanni Cerulli Irelli

F-polynomials and g-vectors

11/08/18 Giovanni Cerulli Irelli

Cluster multiplication formula

11/08/18 Giovanni Cerulli Irelli

Examples of generating extensions

11/08/18 Giovanni Cerulli Irelli

Examples: regular generating extensions

11/08/18 Giovanni Cerulli Irelli

Proof of Theorem 1

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Proof of the theorem

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Cell dec for regular quasi-simples

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Cell dec for regular indecomposables

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Cell dec for regular affine quiver Grassmannians

11/08/18 Giovanni Cerulli Irelli

Cell dec for regular affine quiver Grassmannians

11/08/18 Giovanni Cerulli Irelli

Thm 2: cell dec for affine quiver Grassmannians

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Type Ã

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Type Ã

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Type Ã

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Type Ã

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Type D-tilde

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Type D-tilde

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Type D-tilde

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Type D-tilde

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Type D-tilde: Key Lemma

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Type D-tilde (proof of the Key Lemma)

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Type D-tilde (proof of the Key Lemma)

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Type D-tilde (proof of the Key Lemma)

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Type D-tilde (proof of the Key Lemma)

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Type D-tilde (proof of the Key Lemma)

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Type E-tilde

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Open Problems

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