Generalized line bundles on primitive multiple curves and their moduli

2019/02/25 by Michele Savarese, Savarese, Michele
Mathematics · #14D20 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1902.09463

openalex publication_date 2019/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study generalized line bundles over C_n, a primitive multiple curve of arbitrary multiplicity n, where n is a positive integer. In particular, we give a structure theorem for them and we characterize their semistability in terms of n-1 integral invariants, the indices. These results are used to describe the irreducible components that contain stable generalized line bundles in the Simpson moduli space of semistable sheaves of generalized rank n and fixed generalized degree on C_n. We compute also the dimension of the Zariski tangent space to this moduli space in a point representing a generic generalized line bundle (any generalized line bundle for n=3). In the case n=1 all the results are completely trivial, while the case n=2 has already been treated by Chen and Kass.

Citations

• Coherent Sheaves on Ribbons and their Moduli

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