1,720,973 research outputs found
Hyperelliptic odd coverings
No full textWe investigate a class of odd (ramification) coverings C → P1 where C is hyperelliptic, its Weierstrass points map to one fixed point of P1 and the covering map makes the hyperelliptic involution of C commute with an involution of P1. We compute the number of hyperelliptic odd coverings of minimal degree 4g is when C is general. Our study is approached from three main perspectives: if a fixed effective theta characteristic is fixed they are described as a solution of a certain class of differential equations; then they are studied from the monodromy viewpoint and a deformation argument that leads to the final computation
On coherent sheaves of small length on the affine plane
No full textWe classify coherent modules on k[x, y] of length at most 4 and supported at the origin. We compare our calculation with the motivic class of the moduli stack parametrizing such modules, extracted from the Feit-Fine formula. We observe that the natural torus action on this stack has finitely many fixed points, corresponding to connected skew Ferrers diagrams. (C) 2018 Elsevier Inc. All rights reserved
Monodromy of projections of hypersurfaces
No full textLet X be an irreducible, reduced complex projective hypersurface of degree d. A point P not contained in X is called uniform if the monodromy group of the projection of X from P is isomorphic to the symmetric group Sd. We prove that the locus of non-uniform points is finite when X is smooth or a general projection of a smooth variety. In general, it is contained in a finite union of linear spaces of codimension at least 2, except possibly for a special class of hypersurfaces with singular locus linear in codimension 1. Moreover, we generalise a result of Fukasawa and Takahashi on the finiteness of Galois points
The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces
No full textBrandhorst and Shimada described a large class of Enriques surfaces, called -generic, for which they gave generators for the automorphism groups and calculated the elliptic fibrations and the smooth rational curves up to automorphisms. In the present paper, we give lower bounds for the non-degeneracy invariant of such Enriques surfaces, we show that in most cases the invariant has generic value , and we present the first known example of complex Enriques surface with infinite automorphism group and non-degeneracy invariant not equal to
Hurwitz spaces and liftings to the Valentiner group
No full textView references (23)
We study the components of the Hurwitz scheme of ramified coverings of P1 with monodromy given by the alternating group A6 and elements in the conjugacy class of product of two disjoint cycles. In order to detect the connected components of the Hurwitz scheme, inspired by the case of the spin structures studied by Fried for the 3-cycles, we use as invariant the lifting to the Valentiner group, a triple covering of A6. We prove that the Hurwitz scheme has two irreducible components when the genus of the covering is greater than zero, in accordance with the asymptotic solution found by Bogomolov and Kulikov
Non uniform projections of surfaces in P<sup>3</sup>
Full text linkConsider the projection of a smooth irreducible surface in from a point.The uniform position principle implies that the monodromy group of such a projection from a general point in is the whole symmetric group. We will call such points uniform. Inspired by a result of Pirola and Schlesinger for the case of curves, we proved that the locus of non-uniform points of is at most finite
A computational view on the non-degeneracy invariant for Enriques surfaces
Full text linkFor an Enriques surface , the non-degeneracy invariant
retains information on the elliptic fibrations of and its polarizations. In
the current paper, we introduce a combinatorial version of the non-degeneracy
invariant which depends on together with a configuration of smooth rational
curves, and gives a lower bound for . We provide a SageMath
code that computes this combinatorial invariant and we apply it in several
examples. First we identify a new family of nodal Enriques surfaces satisfying
which are not general and with infinite automorphism group.
We obtain lower bounds on for the Enriques surfaces with eight
disjoint smooth rational curves studied by Mendes Lopes-Pardini. Finally, we
recover Dolgachev and Kond\=o's computation of the non-degeneracy invariant of
the Enriques surfaces with finite automorphism group and provide additional
information on the geometry of their elliptic fibrations.Comment: 26 pages, 11 figures. Final version. To appear in Experimental
Mathematic
- …
