DSpace Collection:
http://hdl.handle.net/10722/257677
2019-05-20T07:25:51ZShifted Poisson geometry and meromorphic matrix algebras over an elliptic curve
http://hdl.handle.net/10722/269246
Title: Shifted Poisson geometry and meromorphic matrix algebras over an elliptic curve
Authors: Hua, Z; Polishchuk, A
Abstract: In this paper we classify symplectic leaves of the regular part of the projectivization of the space of meromorphic endomorphisms of a stable vector bundle on an elliptic curve, using the study of shifted Poisson structures on the moduli of complexes from our previous work cite{HP17}. This Poisson ind-scheme is closely related to the ind Poisson-Lie group associated to Belavin's elliptic r-matrix, studied by Sklyanin, Cherednik and Reyman and Semenov-Tian-Shansky. Our result leads to a classification of symplectic leaves on the regular part of meromorphic matrix algebras over an elliptic curve, which can be viewed as the Lie algebra of the above-mentioned ind Poisson-Lie group. We also describe the decomposition of the product of leaves under the multiplication morphism and show the invariance of Poisson structures under autoequivalences of the derived category of coherent sheaves on an elliptic curve.2017-01-01T00:00:00ZQuasi-homogeneity of superpotentials
http://hdl.handle.net/10722/269244
Title: Quasi-homogeneity of superpotentials
Authors: Hua, Z; Zhou, GS
Abstract: In this article, we study the quasi-homogeneity of a superpotential in a complete free algebra over an algebraic closed field of characteristic zero. We prove that a superpotential with finite dimensional Jacobi algebra is right equivalent to a weighted homogeneous superpotential if and only if the corresponding class in the 0-th Hochschlid homology group of the Jacobi algebra is zero. This result can be viewed as a noncommutative version of the famous theorem of Kyoji Saito on isolated hypersurface singularities.2018-01-01T00:00:00ZModuli 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