Algebraic geometry codes from polyhedral divisors [PDF]
Journal of Symbolic Computation, 2010 AbstractA description of complete normal varieties with lower-dimensional torus action has been given by Altmann et al. (2008), generalizing the theory of toric varieties. Considering the case where the acting torus T has codimension one, we describe T-invariant Weil and Cartier divisors and provide formulae for calculating global sections ...
Suess, Hendrik +2 more
openaire +4 more sources
Singularities of theta divisors in algebraic geometry
, 2012 22 pages, AMS ...
Sebastian Casalaina‐Martin
openaire +4 more sources
Enumerative geometry of surfaces and topological strings [PDF]
International Journal of Modern Physics A, 2022 This survey covers recent developments on the geometry and physics of Looijenga pairs, namely pairs $(X,D)$ with $X$ a complex algebraic surface and $D$ a singular anticanonical divisor in it.
A. Brini
semanticscholar +1 more source
On homological mirror symmetry for the complement of a smooth ample divisor in a K3 surface [PDF]
Kyoto Journal of Mathematics, 2021 We introduce a conjecture on homological mirror symmetry relating the symplectic topology of the complement of a smooth ample divisor in a K3 surface to algebraic geometry of type III degenerations, and prove it when the degree of the divisor is either 2
Yankı Lekili, K. Ueda
semanticscholar +1 more source
Interactive oracle proofs of proximity to algebraic geometry codes [PDF]
Electron. Colloquium Comput. Complex., 2020 In this work, we initiate the study of proximity testing to Algebraic Geometry (AG) codes. An AG code C = C(X, P, D) over an algebraic curve X is a vector space associated to evaluations on P ⊆ X of functions in the Riemann-Roch space LX (D). The problem
Sarah Bordage +3 more
semanticscholar +1 more source
Correspondences between convex geometry and complex geometry [PDF]
Épijournal de Géométrie Algébrique, 2017 We present several analogies between convex geometry and the theory of holomorphic line bundles on smooth projective varieties or K\"ahler manifolds. We study the relation between positive products and mixed volumes.
Brian Lehmann, Jian Xiao
doaj +1 more source
Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor [PDF]
Journal of Algebraic Geometry, 2020 We give a criterion for the projectivisation of a reflexive sheaf on a klt space to be induced by a projective representation of the fundamental group of the smooth locus.
D. Greb, Stefan Kebekus, T. Peternell
semanticscholar +1 more source
On asymptotic base loci of relative anti-canonical divisors of algebraic fiber spaces [PDF]
Journal of Algebraic Geometry, 2020 In this paper, we study the relative anti-canonical divisor − K X / Y -K_{X/Y} of an algebraic fiber space ϕ : X → Y \phi \colon X\to Y , and we reveal relations among positivity conditions of − K
Sho Ejiri, M. Iwai, Shin-ichi Matsumura
semanticscholar +1 more source
Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces [PDF]
Contemporary Mathematics, 2019 We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus.
Y. Aubry +3 more
semanticscholar +1 more source
The Calogero-Franc¸oise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem [PDF]
Integrable Systems and Algebraic Geometry, 2018 We review the Calogero-Francoise integrable system, which is a generalization of the Camassa-Holm system. We express solutions as (twisted) Higgs bundles, in the sense of Hitchin, over the projective line.
S. Rayan, Thomas Stanley, J. Szmigielski
semanticscholar +1 more source