Orders on surfaces provide a rich source of examples of noncommutative surfaces. In [HS05] the authors prove the existence of the analogue of the Picard scheme for orders and in [CK11] the Picard scheme is explicitly computed for an order on P2 ramified on a smooth quartic. In this paper, we continue this line of work, by studying the Picard and Hilbert schemes for an order on P2 ramified on a ...

Let X be a K3 surface which is intersection of three (a net P) of quadrics in P. The curve of degenerate quadrics has degree 6 and defines a double covering of P K3 surface Y ramified in this curve. This is the classical example of a correspondence between K3 surfaces which is related with moduli of vector bundles on K3 studied by Mukai. When general (for fixed Picard lattices) X and Y are isom...

We give model-theoretic accounts and proofs of the following results: Suppose ∂y = Ay is a linear differential equation over a differential field K of characteristic 0, and the field CK of constants of K is existentially closed in K. Then: (i) There exists a Picard-Vessiot extension L of K, namely a differential field extension L of K which is generated by a fundamental system of solutions of t...

Smooth complex Fano varieties of dimension n form a limited family, so they have only a finite number of possible topological types. However not much is known about their topological invariants in higher dimensions. In particular we consider here the second Betti number b2 of a smooth Fano variety X, which coincides with the Picard number ρX . Recall that a Del Pezzo surface S has ρS ≤ 9. Fano ...

Let X be a K3 surface which is intersection of three (i.e. a net P) of quadrics in P. The curve of degenerate quadrics has degree 6 and defines a natural double covering Y of P ramified in this curve which is again a K3. This is a classical example of a correspondence between K3 surfaces which is related with moduli of sheaves on K3’s studied by Mukai. When general (for fixed Picard lattices) X...

We address the usefulness of the unstable manifold correction (UMC) in a Picard iteration for the solution of the velocity field in higher-order ice-flow models. We explain underand overshooting and how one can remedy them. We then discuss the rationale behind the UMC, initially developed to remedy overshooting, and how it was previously introduced in a Picard iteration to calculate the velocit...

The goal of this lecture is to explain in detail the statement that a Picard groupoid is “the same thing as” an Ω-spectrum E with πi(E) = 0 for i 6= 0, 1. Along the way we introduce the notion of a (very special) Γ-space, which provides one of the possible ways of formalising the concept of an “abelian group structure defined up to all the higher homotopies”, and we present an approach to K-the...

This paper 1 introduces a new line of research which ensures soundness and completeness in Natural Language text planners on top of an efficient control strategy. The work builds on the HUNTER-GATItERER analysis system (Beale. 96; Beale & Nirenburg, 96). That system employs constraint satisfaction, branch-and-bound and solution synthesis techniques to produce near linear-time processing for kno...

0