DSpace Collection:
http://hdl.handle.net/10722/257677
2019-02-21T14:38:34ZModuli spaces of ten-line arrangements with double and triple points
http://hdl.handle.net/10722/257972
Title: Moduli spaces of ten-line arrangements with double and triple points
Authors: Amram, M; Cohen, M; Teicher, M; Ye, F
Abstract: Two arrangements with the same combinatorial intersection lattice but whose complements have different fundamental groups are called a Zariski pair. This work finds that there are at most nine such pairs amongst all ten line arrangements whose intersection points are doubles or triples. This result is obtained by considering the moduli space of a given configuration table which describes the intersection lattice. A complete combinatorial classification is given of all arrangements of this type under a suitable assumption, producing a list of seventy-one described in a table, most of which do not explicitly appear in the literature. This list also includes other important counterexamples: nine combinatorial arrangements that are not geometrically realizable.2013-01-01T00:00:00ZShifted Poisson structures and moduli spaces of complexes
http://hdl.handle.net/10722/257678
Title: Shifted Poisson structures and moduli spaces of complexes
Authors: Hua, Z; Polishchuk, A
Abstract: In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety X via derived algebraic geometry. We prove that if X is a Calabi-Yau variety of dimension d then this moduli stack has a (1−d)-shifted Poisson structure. In the case d=1, we construct a natural foliation of the moduli stack by 0-shifted symplectic substacks. We show that our construction recovers various known Poisson structures associated to complex elliptic curves, including the Poisson structure on Hilbert scheme of points on elliptic quantum projective planes studied by Nevins and Stafford, and the Poisson structures on the moduli spaces of stable triples over an elliptic curves considered by one of us. We also relate the latter Poisson structures to the semi-classical limits of the elliptic Sklyanin algebras studied by Feigin and Odesskii.2017-01-01T00:00:00Z