6 M ay 2 00 3 Non - proper value set and the Jacobian condition
نویسنده
چکیده
The non-proper value set of a nonsingular polynomial map from C 2 into itself, if non-empty, must be a curve with one point at infinity. 2000 Mathematical Subject Classification: 14 H07, 14R15.
منابع مشابه
ar X iv : 0 70 7 . 46 02 v 3 [ m at h . A G ] 3 M ay 2 00 8 Geometry of the Theta Divisor of a compactified Jacobian
The object of this paper is the theta divisor of the compactified Jacobian of a nodal curve. We determine its irreducible components and give it a geometric interpretation. A characterization of hyperelliptic irreducible stable curves is appended as an application.
متن کاملM ay 2 00 8 PRYM - TYURIN VARIETIES USING SELF - PRODUCTS OF GROUPS
Given Prym-Tyurin varieties of exponent q with respect to a finite group G, a subgroup H and a set of rational irreducible representations of G satisfying some additional properties, we construct a Prym-Tyurin variety of exponent [G : H ]q in a natural way. We study an example of this result, starting from the dihedral group Dp for any odd prime p. This generalizes the construction of [4] for p...
متن کامل1 1 M ay 2 00 4 Singularities of the Prym Theta Divisor
For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym varieties. Applications of this theorem to cubic threefolds, and Prym varieties of dimension five, are also considered.
متن کاملar X iv : m at h / 01 05 23 2 v 1 [ m at h . N T ] 2 8 M ay 2 00 1 MODULAR CURVES OF GENUS 2
We prove that there are exactly 149 genus two curves C defined over Q such that there exists a nonconstant morphism π : X 1 (N) → C defined over Q and the jacobian of C is Q-isogenous to the abelian variety A f attached by Shimura to a newform f ∈ S 2 (Γ 1 (N)). We determine the corresponding newforms and present equations for all these curves.
متن کاملar X iv : m at h / 04 05 08 1 v 1 [ m at h . L O ] 5 M ay 2 00 4 Preserving Preservation
We present preservation theorems for countable support iteration of nep forcing notions satisfying “old reals are not Lebesgue null” (section 6) and “old reals are not meager” (section 5). (Nep is a generalization of Suslin proper.) We also give some results for general Suslin ccc ideals (the results are summarized in a diagram on page 17). This paper is closely related to [She98, XVIII, §3] an...
متن کامل