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We study linear projections on Pluecker space whose restriction to the Grassmannian is a non-trivial branched cover. When an automorphism of the Grassmannian preserves the fibers, we show that the Grassmannian is necessarily of m-dimensional linear subspaces in a symplectic vector space of dimension 2m, and the linear map is the Lagrangian involution. The Wronski map for a self-adjoint linear differential operator and pole placement map for symmetric linear systems are natural examples.
We treat Kollars injectivity theorem from the analytic (or differential geometric) viewpoint. More precisely, we give a curvature condition which implies Kollar type cohomology injectivity theorems. Our main theorem is formulated for a compact Kahler
In this paper we consider the Prym map for double coverings of curves of genus $g$ ramified at $r>0$ points. That is, the map associating to a double ramified covering its Prym variety. The generic Torelli theorem states that the Prym map is generica
Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas, circ
We give an introduction to moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet and Schmitt, and the associated integrals giving rise to gauged Gromov-Witten invariants. We survey various applications to cohomological and K-theoretic Gromov-Witten invariants.
Let $K$ be a number field, let $phi in K(t)$ be a rational map of degree at least 2, and let $alpha, beta in K$. We show that if $alpha$ is not in the forward orbit of $beta$, then there is a positive proportion of primes ${mathfrak p}$ of $K$ such t