325 research outputs found
Stable Degenerations of Surfaces Isogenous to a Product II
In this note, we describe the possible singularities on a stable surface
which is in the boundary of the moduli space of surfaces isogenous to a
product. Then we use the -Gorenstein deformation theory to get some
connected components of the moduli space of stable surfaces.Comment: 17 pages; the preliminary part is made more concise. Accecpted by
Transactions of the American Mathematical Societ
On a generalized canonical bundle formula for generically finite morphisms
We prove a canonical bundle formula for generically finite morphisms in the
setting of generalized pairs (with -coefficients). This complements
Filipazzi's canonical bundle formula for morphisms with connected fibres. It is
then applied to obtain a subadjunction formula for log canonical centers of
generalized pairs. As another application, we show that the image of an
anti-nef log canonical generalized pair has the structure of a numerically
trivial log canonical generalized pair. This readily implies a result of
Chen--Zhang. Along the way we prove that the Shokurov type convex sets for
anti-nef log canonical divisors are indeed rational polyhedral sets.Comment: 29 pages, to appear in Ann. Inst. Fourier (Grenoble
Automorphisms of surfaces of general type with q>=2 acting trivially in cohomology
A compact complex manifold X is said to be rationally cohomologically
rigidified if its automorphism group Aut(X) acts faithfully on the cohomology
ring H*(X,Q). In this note, we prove that, surfaces of general type with
irregularity q>2 are rationally cohomologically rigidified, and so are minimal
surfaces S with q=2 unless K^2=8X. This answers a question of Fabrizio Catanese
in part.
As examples we give a complete classification of surfaces isogenous to a
product with q=2 that are not rationally cohomologically rigidified. These
surfaces turn out however to be rigidified.Comment: 18 pages; a remark and a closely relevant reference are adde
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