Results 11 to 20 of about 310,925 (271)

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

The construction problem for Hodge numbers modulo an integer in positive characteristic

Forum of Mathematics, Sigma, 2020
Let k be an algebraically closed field of positive characteristic. For any integer $m\ge 2$ , we show that the Hodge numbers of a smooth projective k-variety can take on any combination of values modulo m, subject only to Serre duality.
Remy van Dobben de Bruyn, Matthias Paulsen   +1 more
doaj   +1 more source

Explicit equations of the Cartwright-Steger surface [PDF]

Épijournal de Géométrie Algébrique, 2020
We construct explicit equations of Cartwright-Steger and related surfaces.
Lev A. Borisov, Sai-Kee Yeung
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

Formalization and Implementation of Algebraic Methods in Geometry [PDF]

Electronic Proceedings in Theoretical Computer Science, 2012
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools.
Filip Marić, Ivan Petrović, Danijela Petrović, Predrag Janičić   +3 more
doaj   +1 more source

Factorization of the Abel-Jacobi maps [PDF]

Épijournal de Géométrie Algébrique, 2021
As an application of the theory of Lawson homology and morphic cohomology, Walker proved that the Abel-Jacobi map factors through another regular homomorphism. In this note, we give a direct proof of the theorem.
Fumiaki Suzuki
doaj   +1 more source

How to glue derived categories

Bulletin of Mathematical Sciences, 2018
We give an overview of existing enhancement techniques for derived and trianguated categories based on the notion of a stable model category, and show how it can be applied to the problem of gluing triangulated categories.
D. Kaledin
doaj   +1 more source

Hyperelliptic classes are rigid and extremal in genus two [PDF]

Épijournal de Géométrie Algébrique, 2020
We show that the class of the locus of hyperelliptic curves with $\ell$ marked Weierstrass points, $m$ marked conjugate pairs of points, and $n$ free marked points is rigid and extremal in the cone of effective codimension-($\ell + m$) classes on ...
Vance Blankers
doaj   +1 more source

Algebraic Geometry over Heyting Algebras [PDF]

Journal of Siberian Federal University. Mathematics & Physics, 2020
In this article, we study the algebraic geometry over Heyting algebras and we investigate the properties of being equationally Noetherian and qω-compact over such ...
openaire   +2 more sources