The birational type of the moduli space of even spin curves

By G. Farkas. 2008

54 citations recorded by the source corpus.

Abstract We determine the Kodaira dimension of the moduli space S g of even spin curves for all g. Precisely, we show that S g is of general type for g > 8 and has negative Kodaira dimension for g 8 .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bfd6e99ec3cb2215df36631aa4f1a0df14096958

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Citations in the corpus

Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus (2011, methodology): “λ−δ other for g= 3. The theta-null divisor. Consider the divisor Θ ⊂ Mg,1 parameterizing (X,p) such that Xadmits an odd theta characteristic whose support contains p. The class of Θ was calculated in [Far10], which specializes as follows: (3) Θ = 30λ+60ω rel −4δ 0 −δ other for g= 4. The Brill-Noethe”
The Picard group of the moduli space of curves with level structures (2009, background): “is g-dimensional,so we have a complexline bundleλg =∧g hg. ArbarelloCornalba [1] showed that Pic(Mg)=hλgi. Divisibility. Let λg(L)∈Pic(Mg(L)) be the pullback of λg. It was recently shown by G. Farkas [20] that for L even, the line bundle λg(L)has a fourth root modulo torsion. More precisely, there e”
THE MODULI SPACE OF TWISTED CANONICAL DIVISORS (2015, background): “On the other hand, the component Hg(2) maps with 1 dimensional fibers over the divisor 2null of curves with a vanishing theta-null, see [12].”
The geometry of the moduli space of odd spin curves (2010, background): “remal pointof theeffective coneof divisors sothat thecoefﬁcients α,β stand a chance of being positive. In the case of S+ g , the role of D is played by the divisor Θnull of vanishing theta-nulls, see [F3]. In the case of S− g we compute the class of degenerate theta-characteristics, that is, curves ”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, result): “ 0 +2β 0) , where N:= deg(G1 k/M 0 g) = (2k−2)! k!(k−1)! 11 denotes the Catalan number of linear series g1 k on a general curve of genus 2k− 2. This yields yet another proof of the main result from [F2], in the sense that we compute the class of the divisor Θ null of vanishing theta-nulls: σ∗(Z 1(χ”