50,699 research outputs found
Birational Geometry of Singular Moduli Spaces of O'Grady Type
Following Bayer and Macr\`{i}, we study the birational geometry of singular
moduli spaces of sheaves on a K3 surface which admit symplectic
resolutions. More precisely, we use the Bayer-Macr\`{i} map from the space of
Bridgeland stability conditions to the cone of movable
divisors on to relate wall-crossing in to birational
transformations of . We give a complete classification of walls in
and show that every birational model of obtained by
performing a finite sequence of flops from appears as a moduli space of
Bridgeland semistable objects on . An essential ingredient of our proof is
an isometry between the orthogonal complement of a Mukai vector inside the
algebraic Mukai lattice of and the N\'{e}ron-Severi lattice of which
generalises results of Yoshioka, as well as Perego and Rapagnetta. Moreover,
this allows us to conclude that the symplectic resolution of is deformation
equivalent to the 10-dimensional irreducible holomorphic symplectic manifold
found by O'Grady.Comment: Final versio
Geometry of lines and degeneracy loci of morphisms of vector bundles
Corrado Segre played a leading role in the foundation of line geometry. We
survey some recent results on degeneracy loci of morphisms of vector bundles
where he still is of profound inspiration.Comment: 10 pages. To appear in the proceedings of the conference "Homage to
Corrado Segre
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