331 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
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