Components of moduli spaces of spin curves with the expected codimension

Benzo, Luca

doi:10.1007/s00208-015-1171-6

Cited by 4 publications

(20 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Components of M r g having expected dimension. We summarize and slightly improve some of the results included in [4], where the sharpness of Harris' bound is proved.…”

Section: Existence Of Components With Expected Dimensionmentioning

confidence: 81%

“…Actually, the proof shall be mainly set in the Hilbert scheme Hilb r g(r),g(r)−1 of curves of arithmetic genus g(r) and degree g(r) − 1 in P r , with at most nodes as singularities. Section 3.1 shall concern the main results of [4], assuring the existence of an irreducible component W r g(r) ⊂ Hilb r g(r),g(r)−1 whose general point is a smooth curve C ⊂ P r such that O C (1) is a large theta-characteristic. Moreover, we shall slightly improve the description of curves parameterized over W r g(r) .…”

Section: Existence Of Components With Expected Dimensionmentioning

confidence: 99%

“…, 1) is well-known for small values of r (cf. [24]), and it is included in [4, Theorem 1.2] for arbitrary r. In particular, the value of g(r) can be lowered in this case (see [11,5]). Besides, the statement in the case k = (g − 1) with 0 ≤ r ≤ 3 is covered by different results in [15,6,3], so Theorem 1.2 extends them to arbitrary large values of r.…”

Section: Introductionmentioning

confidence: 99%

“…As far as arbitrary large values of r are concerned, we argue by induction on g and r separately, in analogy with [11,4] where the sharpness of Harris' bound is proved. Thanks to [3,Theorem 4.1], if g(r) is an integer such that G r g(r) admits an irreducible component Z g(r) having expected dimension, then for any g ≥ g(r), the locus G r g has an irreducible component with the same property.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we consider nodal reducible curves in P r consisting of an elliptic normal curve suitably attached to a degenerate curve C such that [C] ∈ M r−1 g(r−1) . It follows from [4], that these singular curves can be deformed to smooth curves X ⊂ P r such that [X] ∈ M r g(r) , where O X (1) is the corresponding large theta-characteristic. Therefore a pair [X, p] lies on G r g(r) , i.e.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On large theta-characteristics with prescribed vanishing

Ballico

Bastianelli

Benzo

2018

Annali di Matematica

Self Cite

View full text Add to dashboard Cite

Let C be a smooth projective curve of genus g ≥ 2. Fix an integer r ≥ 0, and let k = (k1, . . . , kn) be a sequence of positive integers with n i=1 ki = g − 1.In this paper, we study npointed curves (C, p1, . . . , pn) such that the line bundle L := OC n i=1 kipi is a theta-characteristic with h 0 (C, L) ≥ r + 1 and h 0 (C, L) ≡ r + 1 (mod. 2). We prove that they describe a sublocus G r g (k) of Mg,n having codimension at most g − 1 + r(r−1) 2 . Moreover, for any r ≥ 0, k as above, and g greater than an explicit integer g(r) depending on r, we present irreducible components of G r g (k) attaining the maximal codimension in Mg,n, so that the bound turns out to be sharp.

show abstract

“…Components of M r g having expected dimension. We summarize and slightly improve some of the results included in [4], where the sharpness of Harris' bound is proved.…”

Section: Existence Of Components With Expected Dimensionmentioning

confidence: 81%

Section: Existence Of Components With Expected Dimensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On large theta-characteristics with prescribed vanishing

Ballico

Bastianelli

Benzo

2018

Annali di Matematica

Self Cite

View full text Add to dashboard Cite

show abstract

Subcanonical points on projective curves and triply periodic minimal surfaces in the Euclidean space

Bastianelli

Pirola

2014

Math. Z.

View full text Add to dashboard Cite

A point p on a smooth complex projective curve C of genus g ≥ 3 is subcanonical if the divisor (2g-2)p is canonical. The subcanonical locus in the moduli space M_{g,1} described by pairs (C,p) as above has dimension 2g-1 and consists of three irreducible components. Apart from the hyperelliptic component, the other two components depend on the parity of h^0(C,(g-1)p), and their general points satisfy h^0(C,(g-1)p)=1 and 2, respectively. In this paper, we study the subloci of pairs (C,p) such that h^0(C,(g-1)p) ≥ r+1 and h^0(C,(g-1)p) has the same parity as r+1, for some non-negative integer r. In particular, we provide a lower bound on their dimension, and we prove its sharpness for r ≤ 3. As an application, we further give an existence result for triply periodic minimal surfaces immersed in the 3-dimensional Euclidean space, completing a previous result of the second author

show abstract

On the surjectivity of weighted Gaussian maps

Ballico

Pernigotti

2013

Rend. Circ. Mat. Palermo

View full text Add to dashboard Cite

We study the surjectivity of suitable weighted Gaussian maps γ a,b (X, L) which provide a natural generalization of the standard Gaussian maps and encode the local geometry of the locus Th r g,h ⊂ Mg of curves endowed with an h-th root L of the canonical bundle satisfying h 0 (L) ≥ r + 1. In particular, we get a bound on the dimension of its Zariski tangent space, which turns out to be sharp in the special case r = 0. Finally, we describe this locus in the case of complete intersection curves.

show abstract

Components of moduli spaces of spin curves with the expected codimension

Cited by 4 publications

References 15 publications

On large theta-characteristics with prescribed vanishing

On large theta-characteristics with prescribed vanishing

Subcanonical points on projective curves and triply periodic minimal surfaces in the Euclidean space

On the surjectivity of weighted Gaussian maps

Contact Info

Product

Resources

About