Moduli of Nodal Curves on Smooth Surfaces of General Type
نویسنده
چکیده
In this paper we focus on the problem of computing the number of moduli of the so called Severi varieties (denoted by V|D|,δ), which parametrize universal families of irreducible, δ-nodal curves in a complete linear system |D|, on a smooth projective surface S of general type. We determine geometrical and numerical conditions on D and numerical conditions on δ ensuring that such number coincides with dim(V|D|,δ). As related facts, we also determine some sharp results concerning the geometry of some Severi varieties.
منابع مشابه
Murphy’s Law for the Hilbert scheme (and the Chow variety, and moduli spaces of surfaces of general type, and stable maps, and nodal and cuspidal plane curves, and...)
Murphy’s Law for the Hilbert scheme (and the Chow variety, and moduli spaces of surfaces of general type, and stable maps, and nodal and cuspidal plane curves, and . . . )
متن کاملThe rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces
The purpose of this note is to prove the rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers. A Coble surface is a rational surface obtained by blowing up 10 nodes of a rational plane curve of degree 6, and an Enriques surface is said to be nodal if it contains a smooth rational curve. The moduli space of nodal Enriques surfaces is...
متن کاملQUOTIENTS OF PRODUCTS OF CURVES, NEW SURFACES WITH pg = 0 AND THEIR FUNDAMENTAL GROUPS
We construct many new surfaces of general type with q = pg = 0 whose canonical model is the quotient of the product of two curves by the action of a finite group G, constructing in this way many new interesting fundamental groups which distinguish connected components of the moduli space of surfaces of general type. We indeed classify all such surfaces whose canonical model is singular (the smo...
متن کاملOn The Moduli of Surfaces Admitting Genus Two Fibrations Over Elliptic Curves
In this paper, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two fibrations over elliptic curves. We observe that, a surface admitting a smooth fibration as above is elliptic and we employ results on the moduli of polarized elliptic surfaces, to construct moduli spaces of these smooth fibrations. In the case of nonsmooth fibrations, we...
متن کاملIsogenous to a Product of Curves
A smooth algebraic surface S is isogenous to a product, not of mixed type, if there exist two smooth curves C, F and a finite group G, acting faithfully on both C and F and freely on their product, so that S = (C × F )/G. In this paper we classify the surfaces of general type with pg = q = 1 which are isogenous to an unmixed product, assuming that the group G is abelian. It turns out that they ...
متن کامل