3,837 research outputs found
On plane sextics with double singular points
We compute the fundamental groups of five maximizing sextics with double
singular points only; in four cases, the groups are as expected. The approach
used would apply to other sextics as well, given their equations.Comment: A few explanations and references adde
Kummer covers and braid monodromy
In this work we describe a method to reconstruct the braid monodromy of the
preimage of a curve by a Kummer cover. This method is interesting, since it
combines two techniques, namely, the reconstruction of a highly non-generic
braid monodromy with a systematic method to go from a non-generic to a generic
braid monodromy. This "generification" method is independent from Kummer covers
and can be applied in more general circumstances since non generic braid
monodromies appear more naturally and are oftentimes much easier to compute.
Explicit examples are computed using these techniques.Comment: 34 pages, 16 figure
Culture and cultures in tourism
In this special issue of Anatolia, we explore a number of new trends and
products related to cultural tourism, searching for a deeper understanding of
how culture is becoming a central factor of attraction in tourism. Contributed
papers deal with a number of on-going trends in cultural tourism, including
the importance of heritage valuing for sustainability of destinations, the
raising wave of religious travels in Arab countries recently opening to
tourism, or the analysis of interactions between cultural visitors and local
residentsThis work was supported by Groups of Excellence Program of Fundación Séneca, Science and Technology Agency of the Region of Murcia [project number 19884/GERM/15
Cartier and Weil Divisors on Varieties with Quotient Singularities
The main goal of this paper is to show that the notions of Weil and Cartier
-divisors coincide for -manifolds and give a procedure to
express a rational Weil divisor as a rational Cartier divisor. The theory is
illustrated on weighted projective spaces and weighted blow-ups.Comment: 16 page
On fundamental groups of plane curve complements
In this paper we discuss some properties of fundamental groups and Alexander
polynomials of plane curves. We discuss the relationship of the non-triviality
of Alexander polynomials and the notion of (nearly) freeness for irreducible
plane curves. We reprove and restate in modern terms a somewhat forgotten
result of Zariski. Finally, we describe some topological properties of curves
with abelian fundamental group
Number of Jordan blocks of the maximal size for local monodromies
We prove formulas for the number of Jordan blocks of the maximal size for
local monodromies of one-parameter degenerations of complex algebraic varieties
where the bound of the size comes from the monodromy theorem. In case the
general fibers are smooth and compact, the proof calculates some part of the
weight spectral sequence of the limit mixed Hodge structure of Steenbrink. In
the singular case, we can prove a similar formula for the monodromy on the
cohomology with compact supports, but not on the usual cohomology. We also show
that the number can really depend on the position of singular points in the
embedded resolution even in the isolated singularity case, and hence there are
no simple combinatorial formulas using the embedded resolution in general.Comment: 23 page
Effective invariants of braid monodromy and topology of plane curves
In this paper we construct effective invariants for braid monodromy of affine
curves. We also prove that, for some curves, braid monodromy determines their
topology. We apply this result to find a pair of curves with conjugate
equations in a number field but which do not admit any orientation-preserving
homeomorphism.Comment: 26 pages, two EPS figures, LaTe
On the connection between fundamental groups and pencils with multiple fibers
We present two results about the relationship between fundamental groups of
quasiprojective manifolds and linear systems on a projectivization. We prove
the existence of a plane curve with non-abelian fundamental group of the
complement which does not admit a mapping onto an orbifold with non-abelian
fundamental group. We also find an affine manifold whose irreducible components
of its characteristic varieties do not come from the pull-back of the
characteristic varieties of an orbifold
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