Let S be the first degeneracy locus of a morphism vector bundles corresponding to general matrix linear forms in $${\mathbb {P}}^s$$ . We prove that, under certain positivity conditions, its Hilbert square $${{\mathrm{Hilb}}}^2(S)$$ is isomorphic zero global section an irreducible homogeneous bundle on product Grassmannians. Our construction involves naturally associated Fano variety, and expli...

In systems with strong electron-lattice coupling, such as manganites, orbital degeneracy is lifted, causing a null expectation value of the orbital magnetic moment. Magnetic structure is thus determined by spin-spin superexchange. In titanates, however, with much smaller Jahn-Teller distortions, orbital degeneracy might allow non-zero values of the orbital magnetic moment, and novel forms of fe...

The pyrochlore lattice Heisenberg antiferromagnet has a massive classical ground state degeneracy. We summarize three approximation schemes, valid for large spin length S, to capture the (partial) lifting of this degeneracy when zero-point quantum fluctuations are taken into account; all three are related to analytic loop expansions. The first is harmonic order spin waves; at this order, there ...