Zobrazeno 1 - 10
of 942
pro vyhledávání: '"Cox rings"'
Autor:
Francone, Luca
We construct a graded cluster algebra structure on the Cox ring of a smooth complex variety $Z$, depending on a base cluster structure on the ring of regular functions of an open subset $Y$ of $Z$. After considering some elementary examples of our co
Externí odkaz:
http://arxiv.org/abs/2412.04173
Autor:
Hubbard, Austin
We construct and enumerate all crepant resolutions of hyperpolygon spaces, a family of conical symplectic singularities arising as Nakajima quiver varieties associated to a star-shaped quiver. We provide an explicit presentation of the Cox ring of an
Externí odkaz:
http://arxiv.org/abs/2406.04117
This paper deals with the problem of computing a generating set for the Cox ring $R(X)$ of a smooth projective rational surface $X$ with nef anticanonical class. In case $R(X)$ is finitely generated, we show that the degrees of its generators are eit
Externí odkaz:
http://arxiv.org/abs/2403.09945
Let $X^{1,n}_r$ be the blow-up of $\mathbb{P}^1\times\mathbb{P}^n$ in $r$ general points. We describe the Mori cone of $X^{1,n}_r$ for $r\leq n+2$ and for $r = n+3$ when $n\leq 4$. Furthermore, we prove that $X^{1,n}_{n+1}$ is log Fano and give an ex
Externí odkaz:
http://arxiv.org/abs/2308.11283
Autor:
González, José Luis, Laface, Antonio
Publikováno v:
Jos\'e Luis Gonz\'alez and Antonio Laface. Finite generation of Cox rings. Notices of the American Mathematical Society. Vol. 69, no. 8 (2022), pp. 1320-1333
In this expository note we discuss a class of graded algebras named Cox rings, which are naturally associated to algebraic varieties generalizing the homogeneous coordinate rings of projective spaces. Whenever the Cox ring is finitely generated, the
Externí odkaz:
http://arxiv.org/abs/2209.15633
Autor:
Włodarczyk, Jarosław
We extend the Cox-Hu-Keel construction of the Cox rings to any proper birational morphisms of normal noetherian schemes. It allows the representation of any proper birational morphism by a map of schemes with mild singularities with torus actions. In
Externí odkaz:
http://arxiv.org/abs/2301.12452
Autor:
Belotti, Mara, Panizzut, Marta
We prove quadratic generation for the ideal of the Cox ring of the blow-up of $\mathbb{P}^3$ at $7$ points, solving a conjecture of Lesieutre and Park. To do this we compute Khovanskii bases, implementing techniques which proved successful in the cas
Externí odkaz:
http://arxiv.org/abs/2208.05258
Autor:
George, Courtney, Manon, Christopher
Work of Gonz\'alez, Hering, Payne, and S\"uss shows that it is possible to find both examples and non-examples of Mori dream spaces among projectivized toric vector bundles. This result, and the combinatorial nature of the data of projectivized toric
Externí odkaz:
http://arxiv.org/abs/2205.10147