Results 11 to 20 of about 7,186 (267)

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc   +2 more sources

Limits of the trivial bundle on a curve [PDF]

Épijournal de Géométrie Algébrique, 2018
We attempt to describe the rank 2 vector bundles on a curve C which are specializations of the trivial bundle. We get a complete classifications when C is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit vector bundles are ...
Arnaud Beauville
doaj   +1 more source

On the group of zero-cycles of holomorphic symplectic varieties [PDF]

Épijournal de Géométrie Algébrique, 2020
For a moduli space of Bridgeland-stable objects on a K3 surface, we show that the Chow class of a point is determined by the Chern class of the corresponding object on the surface.
Alina Marian, Xiaolei Zhao
doaj   +1 more source

Smoothability of relative stable maps to stacky curves [PDF]

Épijournal de Géométrie Algébrique, 2023
Using log geometry, we study smoothability of genus zero twisted stable maps to stacky curves relative to a collection of marked points. One application is to smoothing semi-log canonical fibered surfaces with marked singular fibers.
Kenneth Ascher, Dori Bejleri
doaj   +1 more source

Refined Verlinde formulas for Hilbert schemes of points and moduli spaces of sheaves on K3 surfaces [PDF]

Épijournal de Géométrie Algébrique, 2020
We compute generating functions for elliptic genera with values in line bundles on Hilbert schemes of points on surfaces. As an application we also compute generating functions for elliptic genera with values in determinant line bundles on moduli spaces ...
Lothar Göttsche
doaj   +1 more source

On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties [PDF]

Épijournal de Géométrie Algébrique, 2023
We prove that the rational Chow motive of a six dimensional hyper-K\"{a}hler variety obtained as symplectic resolution of O'Grady type of a singular moduli space of semistable sheaves on an abelian surface $A$ belongs to the tensor category of motives ...
Salvatore Floccari
doaj   +1 more source

Abundance for slc surfaces over arbitrary fields [PDF]

Épijournal de Géométrie Algébrique, 2023
We prove the abundance conjecture for projective slc surfaces over arbitrary fields of positive characteristic. The proof relies on abundance for lc surfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon and Xu to descend semi ...
Quentin Posva
doaj   +1 more source

Stably semiorthogonally indecomposable varieties [PDF]

Épijournal de Géométrie Algébrique, 2023
A triangulated category is said to be indecomposable if it admits no nontrivial semiorthogonal decompositions. We introduce a definition of a noncommutatively stably semiorthogonally indecomposable (NSSI) variety. This propery implies, among other things,
Dmitrii Pirozhkov
doaj   +1 more source

Double spinor Calabi-Yau varieties [PDF]

Épijournal de Géométrie Algébrique, 2019
Consider the ten-dimensional spinor variety in the projectivization of a half-spin representation of dimension sixteen. The intersection X of two general translates of this variety is a smooth Calabi-Yau fivefold, as well as the intersection Y of their ...
Laurent Manivel
doaj   +1 more source

A characterization of finite \'etale morphisms in tensor triangular geometry [PDF]

Épijournal de Géométrie Algébrique, 2022
We provide a characterization of finite \'etale morphisms in tensor triangular geometry. They are precisely those functors which have a conservative right adjoint, satisfy Grothendieck--Neeman duality, and for which the relative dualizing object is ...
Beren Sanders
doaj   +1 more source