65 research outputs found
Involutions on a surface of general type with ,
In this paper we study on the involution on minimal surfaces of general type
with and . We focus on the classification of the birational
models of the quotient surfaces and their branch divisors induced by an
involution.Comment: 16 pages, There are small modifications in Introduction and in
Section 5. These modifications do not affect our main result of
classification (Theorem and Classification Table in Introduction
Deformation of a generically finite map to a hypersurface embedding
Motivated by the theory of Inoue-type varieties, we give a structure theorem
for projective manifolds with the property of admitting a 1-parameter
deformation where is a hypersurface in a projective smooth manifold
.
Their structure is the one of special iterated univariate coverings which we
call of normal type, which essentially means that the line bundles where the
univariate coverings live are tensor powers of the normal bundle to the image
of .
We give applications to the case where is projective space,
respectively an Abelian variety.Comment: 14 pages, final version to appear on Journal Mathematiques Pures
Appliquees (Journal de Liouville
Log minimal model program for the moduli space of stable curves of genus three
In this paper, we completely work out the log minimal model program for the
moduli space of stable curves of genus three. We employ a rational multiple
of the divisor of singular curves as the boundary
divisor, construct the log canonical model for the pair using geometric invariant theory as we vary from one to
zero, and give a modular interpretation of each log canonical model and the
birational maps between them. By using the modular description, we are able to
identify all but one log canonical models with existing compactifications of
, some new and others classical, while the exception gives a new modular
compactification of .Comment: 35 pages, 6 figure
Exceptional collections on Dolgachev surfaces associated with degenerations
Dolgachev surfaces are simply connected minimal elliptic surfaces with
and of Kodaira dimension 1. These surfaces were constructed by
logarithmic transformations of rational elliptic surfaces. In this paper, we
explain the construction of Dolgachev surfaces via -Gorenstein
smoothing of singular rational surfaces with two cyclic quotient singularities.
This construction is based on the paper by Lee-Park. Also, some exceptional
bundles on Dolgachev surfaces associated with -Gorenstein smoothing
are constructed based on the idea of Hacking. In the case if Dolgachev surfaces
were of type , we describe the Picard group and present an exceptional
collection of maximal length. Finally, we prove that the presented exceptional
collection is not full, hence there exist a nontrivial phantom category in the
derived category.Comment: 35 pages; 3 figures; exposition improved; Adv. Math. (to appear
Simply connected surfaces of general type in positive characteristic via deformation theory
Algebraically simply connected surfaces of general type with p_g=q=0 and 1\le
K^2\le 4 in positive characteristic (with one exception in K^2=4) are presented
by using a Q-Gorenstein smoothing of two-dimensional toric singularities, a
generalization of Lee-Park's construction in the field of complex numbers to
the positive characteristic case, and Grothendieck's specialization theorem for
the fundamental group.Comment: 78 pages, 16 figures, Final version will appear in Proc. London Mat
A construction of Horikawa surface via Q-Gorenstein smoothings
In this article we prove that Fintushel-Stern's construction of Horikawa
surface, which is obtained from an elliptic surface via a rational blow-down
surgery in smooth category, can be performed in complex category. The main
technique involved is Q-Gorenstein smoothings.Comment: 10 pages, some corrections and Proposition 3.1 is adde
The Abel-Jacobi map of the space of conics for double sextic threefolds
Let be a double cover of branched along a sextic surface
. In this paper, we show that, for general , the Abel-Jacobi map
associated to the normalization of the surface of curves
contained in which are preimages of lines bitangent to , gives an
isogeny between the Albanese variety of and the intermediate
Jacobian of .Comment: 16 page
On rational maps from the product of two general curves
This paper treats the dominant rational maps from the product of two very
general curves to nonsingular projective surfaces. Combining the result by
Bastianelli and Pirola, we prove that the product of two very general curves of
genus and does not admit dominant rational maps of degree
if the image surface is non-ruled. We also treat the case of the
2-symmetric product of a curve.Comment: 13 pages; exposition improved; Ann. Sc. Norm. Super. Pisa Cl. Sci.
(to appear
Birational contraction of genus two tails in the moduli space of genus four curves I
We show that for , the log canonical model of the pair is isomorphic to the
moduli space of h-semistable curves, and that there is a
birational morphism that contracts the
locus of curves consisting of genus two curves meeting in a
node such that is a Weierstrass point of or . To obtain this
morphism, we construct a compact moduli space of pointed
genus two curves that have nodes, ordinary cusps and tacnodes as singularity,
and prove that it is isomorphic to Rulla's flip constructed in his thesis
Deformations of product-quotient surfaces and reconstruction of Todorov surfaces via -Gorenstein smoothing
We consider the deformation spaces of some singular product-quotient surfaces
, where the curves have genus 3 and the group
is isomorphic to . As a by-product, we give a new construction of
Todorov surfaces with , and by using
-Gorenstein smoothings.Comment: 21 pages, Minor changes are made. It will apper in Advanced Studies
in Pure Mathematics (Proceeding of Algebraic Geometry in East Asia, Taipei
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