Vanishing thetanulls and hyperelliptic curves
نویسنده
چکیده
Let Mg(2) be the moduli space of curves of genus g with a level-2 structure. We prove that there is always a non hyperelliptic element in the intersection of four thetanull divisors in M6(2). We prove also that for all g > 3, each component of the hyperelliptic locus in Mg(2) is a connected component of the intersection of g−2 thetanull divisors.
منابع مشابه
Hyperelliptic Szpiro inequality
We generalize the classical Szpiro inequality to the case of a semistable family of hyperelliptic curves. We show that for a semistable symplectic Lefschetz fibration of hyperelliptic curves of genus g, the number N of non-separating vanishing cycles and the number D of singular fibers satisfy the inequality N ≤ (4g + 2)D.
متن کاملOn Jacobi Inversion Formulae for Telescopic Curves
For a hyperelliptic curve of genus g, it is well known that the symmetric products of g points on the curve are expressed in terms of their Abel–Jacobi image by the hyperelliptic sigma function (Jacobi inversion formulae). Matsutani and Previato gave a natural generalization of the formulae to the more general algebraic curves defined by y = f(x), which are special cases of (n, s) curves, and d...
متن کاملHyperelliptic Lefschetz Fibrations and Branched Covering Spaces
Let M be a smooth 4-manifold which admits a relatively minimal hyperelliptic genus h Lefschetz fibration over S. If all of the vanishing cycles for this fibration are nonseparating curves, then we show that M is a 2-fold cover of an S-bundle over S, branched over an embedded surface. If the collection of vanishing cycles for this fibration includes σ separating curves, we show that M is the rel...
متن کاملThe Coulomb Branch of N = 2 Supersymmetric Product Group Theories from Branes
We determine the low energy description of N = 2 supersymmetric ∏ i SU(ki) gauge theories with bifundamental and fundamental matter based on M-theory fivebrane configurations. The dependence on moduli and scales of the coefficients in the non-hyperelliptic SeibergWitten curves for these theories are determined by considering various field theory and brane limits. A peculiarity in the interpreta...
متن کاملLoci of Curves with Subcanonical Points in Low Genus
Inside the moduli space of curves of genus three with one marked point, we consider the locus of hyperelliptic curves with a marked Weierstrass point, and the locus of nonhyperelliptic curves with a marked hyperflex. These loci have codimension two. We compute the classes of their closures in the moduli space of stable curves of genus three with one marked point. Similarly, we compute the class...
متن کامل