41 research outputs found
The derived category of a non generic cubic fourfold containing a plane
We describe an Azumaya algebra on the resolution of singularities of the
double cover of a plane ramified along a nodal sextic associated to a non
generic cubic fourfold containing a plane. We show that the derived category of
such a resolution, twisted by the Azumaya algebra, is equivalent to the
Kuznetsov component in the semiorthogonal decomposition of the derived category
of the cubic fourfold.Comment: 14 pages, many edits and correction
Fourier-Mukai functors and perfect complexes on dual numbers
We show that every exact fully faithful functor from the category of perfect
complexes on the spectrum of dual numbers to the bounded derived category of a
noetherian separated scheme is of Fourier-Mukai type. The kernel turns out to
be an object of the bounded derived category of coherent complexes on the
product of the two schemes. We also study the space of stability conditions on
the derived category of the spectrum of dual numbers.Comment: 23 pages, Final version to appear in J. Algebr
On coherent sheaves of small length on the affine plane
We classify coherent modules on of length at most 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
Non Uniform Projections of Surfaces in
Consider 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 prove that the locus of
non-uniform points of is at most finite.Comment: 11 pages, no figures. This paper is a result of the work carried out
at PRAGMATIC 2016 Research School. Minor changes and journal references adde
The non-degeneracy invariant of Brandhorst and Shimada families of Enriques surfaces
Brandhorst 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 .Comment: 22 pages, 2 figures. Comments welcome
Alternating Catalan numbers and curves with triple ramification
It is known that the monodromy group of each cover of a general curve of
genus g>3 equals either the symmetric or the alternating group. The classical
Catalan numbers count the minimal degree covers (with symmetric monodromy) of a
general curve of even genus. We solve the analogous problem for the alternating
group and we determine the number of alternating covers of minimal degree 2g+1
of a general curve of genus g.Comment: 18 pages. Minor improvements, also referencing the related work of
Lian. Final version to appear in Annali Scuola Normale di Pis