We study persistence properties of the solution of the Benjamin-Ono equation in weighted Sobolev spaces. Roughly, we show that for beta < 7/2, the solution u(x, t) of the BO remains in the space L-2(|x|(2 beta )dx) if and only if its data u(x, 0) belongs to this space and it is regular enough, i.e. u(0) is an element of H-beta(R).
We show that every projective Oka manifold is elliptic in the sense of Gromov. This gives an affirmative answer to a long-standing open question.
We provide new examples of anti-symplectic involutions on moduli spaces of stable sheaves on K3 surfaces. These involutions are constructed through (anti) autoequivalences of the bounded derived category of coherent sheaves on K3 surfaces arising from spherical bundles. We analyze these induced maps in the moduli space, imposing restrictions on the Mukai vector and considering the preservation of stability conditions. Our construction extends and unifies classical examples, such as the Beauville involutions, Markman-O'Grady reflections and a more recent construction by Beri-Manivel.
In this short note, we will explain that the good moduli space morphisms behave as if they are proper when we consider sheaf operations, though they are not separated. For example, the decomposition theorem and the base change theorem hold for these morphisms, which have applications to the cohomological study of moduli spaces.
We construct exceptional Fano varieties with the smallest known minimal log discrepancies in all dimensions. These varieties are well-formed hypersurfaces in weighted projective space. Their minimal log discrepancies decay doubly exponentially with dimension, and achieve the optimal value in dimension 2.
