DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272019-08-14T19:16:35Z2019-08-14T19:16:35Zl-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficientsHamacher, PaulKim, Wansuhttp://hdl.handle.net/10203/2518972019-03-19T02:01:12ZTitle: l-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
Authors: Hamacher, Paul; Kim, WansuThe regularity of partial elimination ideals, Castelnuovo normality and syzygiesAhn, JeamanKwak, Sijonghttp://hdl.handle.net/10203/2637272019-07-23T02:50:07Z2019-09-01T00:00:00ZTitle: The regularity of partial elimination ideals, Castelnuovo normality and syzygies
Authors: Ahn, Jeaman; Kwak, Sijong
Abstract: Let X be a reduced closed subscheme in P-n, pi : X -> pi(X) subset of Pn-1 be a projection from a point outside X and Z(i) (X) subset of pi(X) be the closed subscheme defined by the i-th partial elimination ideal K-i(I-x), which is supported on the (i + 1)-th multiple points of pi. In this paper, motivated from projection methods to prove Eisenbud-Goto conjecture on regularity in many cases, we describe the syzygetic behaviors and Castelnuovo normality of the projection with a viewpoint of the regularity of the partial elimination ideal K-i(I-X), i >= 1 (or that of the multiple locus Z(i) (X) of pi). We also give some applications to the syzygies and Castelnuovo normality of successive projections, which recover and generalize some known results in [1,3,15,16]. (C) 2019 Published by Elsevier Inc.2019-09-01T00:00:00ZSPIKE LAYER SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM: VARIATIONAL CONSTRUCTION WITHOUT A NONDEGENERACYByeon, JaeyoungMoon, Sang-Hyuckhttp://hdl.handle.net/10203/2503372019-02-20T05:10:58Z2019-07-01T00:00:00ZTitle: SPIKE LAYER SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM: VARIATIONAL CONSTRUCTION WITHOUT A NONDEGENERACY
Authors: Byeon, Jaeyoung; Moon, Sang-Hyuck
Abstract: We consider the following singularly perturbed problem epsilon(2)Delta u - u + f(u) = 0, u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega. Existence of a solution with a spike layer near a min-max critical point of the mean curvature on the boundary partial derivative Omega is well known when a nondegeneracy for a limiting problem holds. In this paper, we use a variational method for the construction of such a solution which does not depend on the nondengeneracy for the limiting problem. By a purely variational approach, we construct the solution for an optimal class of nonlinearities f satisfying the Berestycki-Lions conditions.2019-07-01T00:00:00ZIs a typical bi-Perron algebraic unit a pseudo-Anosov dilatation?Baik, HyungryulRafiqi, AhmadWu, Chenxihttp://hdl.handle.net/10203/2628012019-06-24T02:50:06Z2019-07-01T00:00:00ZTitle: Is a typical bi-Perron algebraic unit a pseudo-Anosov dilatation?
Authors: Baik, Hyungryul; Rafiqi, Ahmad; Wu, Chenxi
Abstract: In this note, we deduce a partial answer to the question in the title. In particular, we show that asymptotically almost all bi-Perron algebraic units whose characteristic polynomial has degree at most 2n do not correspond to dilatations of pseudo-Anosov maps on a closed orientable surface of genus n for n >= 10. As an application of the argument, we also obtain a statement on the number of closed geodesics of the same length in the moduli space of area-one abelian differentials for low-genus cases.2019-07-01T00:00:00Z