Abstract
Here we study the Brill–Noether theory of “extremal” Cornalba’s theta-characteristics on stable curves C of genus g, where “extremal” means that they are line bundles on a quasi-stable model of C with #(Sing(C)) exceptional components.
Highlights
For any integer g ≥ 2 let M g denote the moduli space of stable curves of genus g over an algebraically closed field K such that char(K) = 0
C ∈ M g is equivalent to prescribe the images in Sing(C) of the quasistable model of C on which a Cornalba’s theta-characteristic “is” a line bundle (it is not quite a line bundle L, but a line bundle up-to inessential isomorphisms and we need to prescribe the line bundle L⊗2 ([5], Lemma 2.1 and first part of §3))
None of these problems affect the Brill–Noether theory for the theta-characteristics we will consider in this note
Summary
Components with the expected codimension in the moduli scheme of stable spin curves Abstract. We study the Brill–Noether theory of “extremal” Cornalba’s theta-characteristics on stable curves C of genus g, where “extremal” means that they are line bundles on a quasi-stable model of C with (Sing(C)) exceptional components
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