18 research outputs found
Del Pezzo surfaces of degree 1 and jacobians
We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves,
using Del Pezzo surfaces of degree 1. This paper is a natural continuation of
author's paper math.AG/0405156.Comment: 24 page
2-elementary subgroups of the space Cremona group
We give a sharp bound for orders of elementary abelian 2-groups of birational
automorphisms of rationally connected threefolds
Instanton bundles on Fano threefolds
We introduce the notion of an instanton bundle on a Fano threefold of index
2. For such bundles we give an analogue of a monadic description and discuss
the curve of jumping lines. The cases of threefolds of degree 5 and 4 are
considered in a greater detail.Comment: 31 page, to appear in CEJ
Weakly--exceptional quotient singularities
A singularity is said to be weakly--exceptional if it has a unique purely log
terminal blow up. In dimension , V. Shokurov proved that weakly--exceptional
quotient singularities are exactly those of types , , ,
. This paper classifies the weakly--exceptional quotient singularities
in dimensions and
Rationality of the moduli spaces of plane curves of sufficiently large degree
We prove that the moduli space of plane curves of degree d is rational for
all sufficiently large d.Comment: 18 pages; 1 figure; Macaulay2 scripts used can be found at
http://www.uni-math.gwdg.de/bothmer/rationality/ or at the end of the latex
source fil
Classification of K3-surfaces with involution and maximal symplectic symmetry
K3-surfaces with antisymplectic involution and compatible symplectic actions
of finite groups are considered. In this situation actions of large finite
groups of symplectic transformations are shown to arise via double covers of
Del Pezzo surfaces. A complete classification of K3-surfaces with maximal
symplectic symmetry is obtained.Comment: 26 pages; final publication available at http://www.springerlink.co
Cremona groups of real surfaces
We give an explicit set of generators for various natural subgroups of the real Cremona group Bir(2). This completes and unifies former results by several authors
Homological Mirror Symmetry and Algebraic Cycles
In this chapter we outline some applications of Homological Mirror Symmetry to classical problems in Algebraic Geometry, like rationality of algebraic varieties and the study of algebraic cycles. Several examples are studied in detail