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1. CJM 2012 (vol 65 pp. 905)
Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally we prove a converse to the above statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.
Keywords:threefold, fibration, K3 surface Categories:14J30, 14D06, 14E30, 14J28 |
2. CJM 2011 (vol 64 pp. 845)
Monodromy Filtrations and the Topology of Tropical Varieties We study the topology of tropical varieties that arise from a certain
natural class of varieties. We use the theory of tropical
degenerations to construct a natural, ``multiplicity-free''
parameterization of $\operatorname{Trop}(X)$ by a topological space
$\Gamma_X$ and give a geometric interpretation of the cohomology of
$\Gamma_X$ in terms of the action of a monodromy operator on the
cohomology of $X$. This gives bounds on the Betti numbers of
$\Gamma_X$ in terms of the Betti numbers of $X$ which constrain the
topology of $\operatorname{Trop}(X)$. We also obtain a description of
the top power of the monodromy operator acting on middle cohomology of
$X$ in terms of the volume pairing on $\Gamma_X$.
Categories:14T05, 14D06 |
3. CJM 2003 (vol 55 pp. 839)
Cohomology of Complex Torus Bundles Associated to Cocycles Equivariant holomorphic maps of Hermitian symmetric domains into
Siegel upper half spaces can be used to construct families of
abelian varieties parametrized by locally symmetric spaces, which
can be regarded as complex torus bundles over the parameter spaces.
We extend the construction of such torus bundles using 2-cocycles of
discrete subgroups of the semisimple Lie groups associated to the
given symmetric domains and investigate some of their properties.
In particular, we determine their cohomology along the fibers.
Categories:14K10, 14D06, 14F99 |
4. CJM 2003 (vol 55 pp. 649)
Surfaces with $p_{g}=q=2$ and an Irrational Pencil We describe the irrational pencils on surfaces of general type with
$p_{g}=q=2$.
Categories:14J29, 14J25, 14D06, 14D99 |