arXiv subjects
Publications and source records attributed to Yasunari Nagai.
We explicitly construct a $V$-normal crossing Gorenstein canonical model of the relative symmetric products of a local semistable degeneration of surfaces without a triple point by means of toric geometry. Using this model, we calculate the stringy $E$-polynomial of the relative symmetric product. We also construct a minimal model of degeneration of Hilbert schemes explicitly.
For a semistable degeneration of surfaces without a triple point, we show that two models of degeneration of Hilbert scheme of points of the family, Gulbrandsen-Halle-Hulek degeneration given in [GHH] and the one given by the author in [N], are actually isomorphic.
We give a completely explicit description of the fibers of the natural birational morphism from O'Grady's ten dimensional singular moduli space of sheaves on a K3 surface to the corresponding Donaldson-Uhlenbeck compactification.
We determine the birational geometry of O'Grady's six dimensional example over the Donaldson-Uhlenbeck compactification, by looking at the locus of non-locally-free sheaves on the relevant moduli space.
For a smooth Deligne-Mumford stack over $\CC$, we define its associated Kodaira-Spencer differential graded Lie algebra and show that the deformation functor of the stack is isomorphic to the deformation functor of the Kodaira-Spencer algebra if the stack is proper over $\CC$.
We study the monodromy operators on the betti cohomologies associated to a good degeneration of irreducible symplectic manifold and we show that the unipotency of the monodromy operator on the middle cohomology is at least the half of the dimension.
We give a characterization of irreducible symplectic fourfolds which are given as Hilbert scheme of points on a K3 surface.