1,720,975 research outputs found
Ruled surfaces and generic coverings
No full textIn this paper we show that a neighborhood of a point in a normal complex surface
which admits a projection to the complex plane with branch curve is
obtained by a contracting a section of a ruled surface and quotienting by the action of a finite group.
From this description, we are able to find numerical criteria for the rationality and smoothness of the germ
Chisini's conjecture for curves with singularities of type
No full textWe extend a result by Kulikov on Chisini's conjecture to a broader class of branch curves
A family of surfaces with pg=q=2,K2=7 and Albanese map of degree 3
Full text linkWe study a family of surfaces of general type with pg = q = 2 and K2 = 7, originally constructed by Cancian and Frapporti by using the Computer Algebra System MAGMA. We provide an alternative, computer-free construction of these surfaces, that allows us to describe their Albanese map and their moduli space
A note on a family of surfaces with pg= q= 2 and K2= 7
No full textWe study a family of surfaces of general type with pg= q= 2 and K2= 7 , originally constructed by C. Rito in [35]. We provide an alternative construction of these surfaces, that allows us to describe their Albanese map and the corresponding locus M in the moduli space of surfaces of general type. In particular we prove that M is an open subset, and it has three connected components, all of which are 2-dimensional, irreducible and generically smoot
Generic covers branched over
No full textIn this paper the authors study generic covers of C^2 branched over x^n + y^m = 0 s.t. the total space is a normal analytic surface. They found a complete description of the monodromy of the cover in terms of the monodromy graphs and an almost complete description of the local fundamental groups in case (n, m) = 1. For the general case, they give explicit descriptions of base changes in terms of monodromy graphs; they describe completely the embedded resolution graphs in the case n|m. Via these base changes every cover is a quotient of such a cover
Some evidence for the Coleman–Oort conjecture
No full textThe Coleman-Oort conjecture says that for large g there are no positive-dimensional Shimura subvarieties of A(g) generically contained in the Jacobian locus. Counterexamples are known for g <= 7. They can all be constructed using families of Galois coverings of curves satisfying a numerical condition. These families are already classified in cases where: (a) the Galois group is cyclic, (b) it is abelian and the family is 1-dimensional, or c) g <= 9. By means of carefully designed computations and theoretical arguments excluding a large number of cases we are able to prove that for g <= 100 there are no other families than those already known
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