Zobrazeno 1 - 10
of 133
pro vyhledávání: '"Kasprzyk, Alexander"'
We present an algorithm for growing the denominator $r$ polygons containing a fixed number of lattice points and enumerate such polygons containing few lattice points for small $r$. We describe the Ehrhart quasi-polynomial of a rational polygon in te
Externí odkaz:
http://arxiv.org/abs/2411.19183
Algebraic varieties are the geometric shapes defined by systems of polynomial equations; they are ubiquitous across mathematics and science. Amongst these algebraic varieties are Q-Fano varieties: positively curved shapes which have Q-factorial termi
Externí odkaz:
http://arxiv.org/abs/2310.20458
Publikováno v:
Nat Commun 14, 5526 (2023)
Fano varieties are basic building blocks in geometry - they are `atomic pieces' of mathematical shapes. Recent progress in the classification of Fano varieties involves analysing an invariant called the quantum period. This is a sequence of integers
Externí odkaz:
http://arxiv.org/abs/2309.05473
Fano varieties are 'atomic pieces' of algebraic varieties, the shapes that can be defined by polynomial equations. We describe the role of computation and database methods in the construction and classification of Fano varieties, with an emphasis on
Externí odkaz:
http://arxiv.org/abs/2211.10069
The family of smooth Fano 3-folds with Picard rank 1 and anticanonical volume 4 consists of quartic 3-folds and of double covers of the 3-dimensional quadric branched along an octic surface. They can all be parametrised as complete intersections of a
Externí odkaz:
http://arxiv.org/abs/2210.14781
We describe recent progress in a program to understand the classification of three-dimensional Fano varieties with $\mathbb{Q}$-factorial terminal singularities using mirror symmetry. As part of this we give an improved and more conceptual understand
Externí odkaz:
http://arxiv.org/abs/2210.07328
We explain a web of Sarkisov links that overlies the classification of Fano weighted projective spaces in dimensions 3 and 4, extending results of Prokhorov.
Externí odkaz:
http://arxiv.org/abs/2207.08278
We use machine learning to predict the dimension of a lattice polytope directly from its Ehrhart series. This is highly effective, achieving almost 100% accuracy. We also use machine learning to recover the volume of a lattice polytope from its Ehrha
Externí odkaz:
http://arxiv.org/abs/2207.07717
Autor:
Brown, Gavin, Kasprzyk, Alexander
We explain an effective Kawamata boundedness result for Mori-Fano 3-folds. In particular, we describe a list of 39,550 possible Hilbert series of semistable Mori-Fano 3-folds, with examples to explain its meaning, its relationship to known classifica
Externí odkaz:
http://arxiv.org/abs/2201.07178