Quiver representations arising from degenerations of linear series, II

Esteves E, Santos R, Vital E (Submitted)
ArXiv: 2112.00514 .

Preprint | Eingereicht | Englisch
 
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Esteves, Eduardo; Santos, Renan; Vital, EduardoUniBi
Abstract / Bemerkung
We describe all the schematic limits of families of divisors associated to a given family of rank-r linear series on a one-dimensional family of projective varieties degenerating to a connected reduced projective scheme X defined over any field, under the assumption that the total space of the family is regular along X. More precisely, the degenerating family gives rise to a special quiver Q, called a Zn-quiver, a special representation L of Q in the category of line bundles over X, called a maximal exact linked net, and a special subrepresentation V of the representation H0(X, L) induced from L by taking global sections, called a pure exact finitely generated linked net of dimension r + 1. Given g = (Q, L, V) satisfying these properties, we prove that the quiver Grassmanian LP(V) of subrepresentations of V of pure dimension 1, called a linked projective space, is local complete intersection, reduced and of pure dimension r. Furthermore, we prove that there is a morphism LP(V) → HilbX , and that its image parameterizes all the schematic limits of divisors along the degenerating family of linear series if g arises from one.
Stichworte
Linear Series · Quivers · Quiver Representations
Erscheinungsjahr
2022
Zeitschriftentitel
ArXiv: 2112.00514
Page URI
https://pub.uni-bielefeld.de/record/2987641

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Esteves E, Santos R, Vital E. Quiver representations arising from degenerations of linear series, II. ArXiv: 2112.00514 . Submitted.
Esteves, E., Santos, R., & Vital, E. (Submitted). Quiver representations arising from degenerations of linear series, II. ArXiv: 2112.00514
Esteves, Eduardo, Santos, Renan, and Vital, Eduardo. Submitted. “Quiver representations arising from degenerations of linear series, II”. ArXiv: 2112.00514 .
Esteves, E., Santos, R., and Vital, E. (Submitted). Quiver representations arising from degenerations of linear series, II. ArXiv: 2112.00514 .
Esteves, E., Santos, R., & Vital, E., Submitted. Quiver representations arising from degenerations of linear series, II. ArXiv: 2112.00514 .
E. Esteves, R. Santos, and E. Vital, “Quiver representations arising from degenerations of linear series, II”, ArXiv: 2112.00514 , Submitted.
Esteves, E., Santos, R., Vital, E.: Quiver representations arising from degenerations of linear series, II. ArXiv: 2112.00514 . (Submitted).
Esteves, Eduardo, Santos, Renan, and Vital, Eduardo. “Quiver representations arising from degenerations of linear series, II”. ArXiv: 2112.00514 (Submitted).
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