51
ICRA 2018-Workshop Prague- 7-13 August 2018 Three Lectures on quiver Grassmannians Giovanni Cerulli Irelli

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

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

  • 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.

    11/08/18 Giovanni Cerulli Irelli

  • Image of the strata

    11/08/18 Giovanni Cerulli Irelli

  • Proof of the Lemma

    11/08/18 Giovanni Cerulli Irelli

  • A “nice” stratum in the image

    11/08/18 Giovanni Cerulli Irelli

  • Generating S.E.S.

    11/08/18 Giovanni Cerulli Irelli

  • 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

    11/08/18 Giovanni Cerulli Irelli

  • Proof of the theorem

    11/08/18 Giovanni Cerulli Irelli

  • Cell dec for regular quasi-simples

    11/08/18 Giovanni Cerulli Irelli

  • Cell dec for regular indecomposables

    11/08/18 Giovanni Cerulli Irelli

  • 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

    11/08/18 Giovanni Cerulli Irelli

  • Type Ã

    11/08/18 Giovanni Cerulli Irelli

  • Type Ã

    11/08/18 Giovanni Cerulli Irelli

  • Type Ã

    11/08/18 Giovanni Cerulli Irelli

  • Type Ã

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde: Key Lemma

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde (proof of the Key Lemma)

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde (proof of the Key Lemma)

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde (proof of the Key Lemma)

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde (proof of the Key Lemma)

    11/08/18 Giovanni Cerulli Irelli

  • Type D-tilde (proof of the Key Lemma)

    11/08/18 Giovanni Cerulli Irelli

  • Type E-tilde

    11/08/18 Giovanni Cerulli Irelli

  • Open Problems

    11/08/18 Giovanni Cerulli Irelli