Dominance of a Rational Map to the Coble Quartic
نویسنده
چکیده
We show the dominance of the restriction map from a moduli space of stable sheaves on the projective plane to the Coble sixfold quartic. With the dominance and the interpretation of a stable sheaf on the plane in terms of hyperplane arrangements, we expect these tools to reveal the geometry of the Coble quartic.
منابع مشابه
Plane Quartic Curve in Grassmannians and Dominance of the Restriction Map between Two Moduli Spaces
defined by sending E to E|C . It is shown in [4] that Φk is a dominant map to W,W and W , for k = 1, 2, 3, respectively. In this article, we give a proof of the dominance of the rational map Φ4. This is equivalent to the dominance of the rational map from M(3, 6) to SUC(2, 3KC) by twisting. For a general bundle E ∈ SUC(2, 3KC), we embed C with P2 into a Grassmannian Gr(5, 2) and take the pull-b...
متن کاملThe Moduli Space of Rank-3 Vector Bundles with Trivial Determinant over a Curve of Genus 2 and Duality
Let SUX(3) be the moduli space of semi-stable vector bundles of rank 3 and trivial determinant on a curve X of genus 2. It maps onto P and the map is a double cover branched over a sextic hypersurface called the Coble sextic. In the dual P there is a unique cubic hypersurface, the Coble cubic, singular exactly along the abelian surface of degree 1 line bundles on X. We give a new proof that the...
متن کاملModuli of Plane Quartics, Göpel Invariants and Borcherds Products
ABSTRACT. It is known that the moduli space of plane quartic curves is birational to an arithmetic quotient of a 6-dimensional complex ball ([Kon1]). In this paper, we shall show that there exists a 15-dimensional space of meromorphic automorphic forms on the complex ball which gives a birational embedding of the moduli space of plane quartics with level 2 structure into P. This map coincides w...
متن کاملTwelve Points on the Projective Line, Branched Covers, and Rational Elliptic Fibrations
The following divisors in the space Sym12 P1 of twelve points on P 1 are actually the same: (A) The possible locus of the twelve nodal fibers in a rational elliptic fibration (i.e. a pencil of plane cubic curves); (B) degree 12 binary forms that can be expressed as a cube plus a square; (C) the locus of the twelve tangents to a smooth plane quartic from a general point of the plane; (D) the bra...
متن کاملManin’s Conjecture for Quartic Del Pezzo Surfaces with a Conic Fibration
— An asymptotic formula is established for the number of Q-rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.
متن کامل