On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution

Chapter 1 Introduction......Page 8 Introduction to quivers......Page 12 The path algebra of a quiver......Page 14 Spaces of quiver representations......Page 17 The category of quiver representations......Page 20 Reflection functors......Page 21 Derksen-Weyman technique......Page 23 Domokos-Zubkov technique......Page 25 Schofield-van den Bergh technique......Page 27 Construction of filtered quiver varieties......Page 28 Quiver Grassmannians......Page 29 Quiver flag varieties......Page 30 Filtered quiver varieties......Page 31 Chapter 4 Categories of filtered and graded quiver varieties......Page 35 Filtered quiver varieties associated to finite type ADE Dynkin graphs......Page 48 (Framed) filtered quiver varieties associated to affine Dynkin type Ar......Page 55 Quivers with at most two pathways between any two vertices......Page 67 Other interesting family of quivers......Page 74 Comment regarding at most two pathways......Page 80 Introduction......Page 84 Moduli spaces......Page 86 Geometric invariant theory......Page 87 Hilbert schemes......Page 89 Hamiltonian reduction construction in symplectic geometry......Page 91 Grothendieck-Springer resolution......Page 94 The cotangent bundle of the enhanced Grothendieck-Springer resolution......Page 96 Hamiltonian reduction in stages......Page 99 Orthonormal projection operators in B......Page 101 On the fixed points by the Borel......Page 106 B-orbits on the rss-locus......Page 113 Proof of Proposition rss categorical quotient......Page 116 Changing coordinates......Page 118 B-invariant functions......Page 120 The initial ideal and regular sequence......Page 122 Proof of Proposition rss isomorphism of varieties......Page 123 Extension to a general flag......Page 124 m-Jordan quiver......Page 125 k-Kronecker quiver......Page 126 B-moment map......Page 127 P-moment map......Page 130 References......Page 132