Exterior powers, Polynomial rings and Representation of Lie Algebras / Degenerations of linear series to curves with three components, using quiver representations

Abstract: Young BRAG with two short presentations:

Speaker 1: Ommolbanin Behzad (University of Isfahan, Iran)

Title: Exterior powers, Polynomial rings and Representation of Lie Algebras

Abstract: I will report on some recent work of myself, A. Contiero, D. Martins, R. Vidal Martins about representing lie algebras of vector space endomorphisms on exterior algebras, seeing it as the finite type case of the celebrated DJKM bosonic vertex operator representation of gl∞(Q).

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Speaker 2: Eduardo Vital (IMPA, Brazil)

Title: Degenerations of linear series to curves with three components, using quiver representations

Abstract: We explore the existence of simple bases for certain special quiver representations arising from degenerations of linear series on nodal curves. The existence of a simple basis implies that the representation decomposes into representations of dimension one and simplifies the calculus of the Hilbert polynomial of the quiver Grassmannian associated to the representation. For these quiver representations, we characterise the existence of a simple basis with a local condition. And to a nodal curve with three components we show that its linked projective space is Cohen-Macaulay, reduced, and has pure dimension. This is a joint work in progress with Eduardo Esteves and Renan Santos.

algebraic geometry

Audience: researchers in the topic

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Brazilian algebraic geometry seminar

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