Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Wiśniewski, Jarosław"'
Given an action of the one-dimensional torus on a projective variety, the associated Chow quotient arises as a natural parameter space of invariant $1$-cycles, which dominates the GIT quotients of the variety. In this paper we explore the relation be
Externí odkaz:
http://arxiv.org/abs/2310.18623
Publikováno v:
Math. Z. 304, 45 (2023)
In this paper we study varieties admitting torus actions as geometric realizations of birational transformations. We present an explicit construction of these geometric realizations for a particular class of birational transformations, and study some
Externí odkaz:
http://arxiv.org/abs/2205.08190
Publikováno v:
Rend. Circ. Mat. Palermo (2) 72 (2023), no. 6, 3223-3253
A geometric realization of a birational map $\psi$ among two complex projective varieties is a variety $X$ endowed with a $\mathbb{C}^*$-action inducing $\psi$ as the natural birational map among two extremal geometric quotients. In this paper we stu
Externí odkaz:
http://arxiv.org/abs/2112.15130
Publikováno v:
Eur. J. Math. 8 (2022), no. 3, 1072-1104
We link small modifications of projective varieties with a ${\mathbb C}^*$-action to their GIT quotients. Namely, using flips with centers in closures of Bia{\l}ynicki-Birula cells, we produce a system of birational equivariant modifications of the o
Externí odkaz:
http://arxiv.org/abs/2103.07209
We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on the variety of complete quadrics. This allows us to provide an explicit, basic, albeit of high computationa
Externí odkaz:
http://arxiv.org/abs/2004.07735
Publikováno v:
Selecta Math., 27(10), 2021
We prove LeBrun--Salamon conjecture in the following situation: if $X$ is a contact Fano manifold of dimension $2n+1$ whose group of automorphisms is reductive of rank $\geq \max(2,(n-3)/2)$ then $X$ is the adjoint variety of a simple group. The rank
Externí odkaz:
http://arxiv.org/abs/2004.05971
Publikováno v:
J. Algebraic Geom. 32 (2023), 1-57
In this paper we study smooth projective varieties and polarized pairs with an action of a one dimensional complex torus. As a main tool, we define birational geometric counterparts of these actions, that, under certain assumptions, encode the inform
Externí odkaz:
http://arxiv.org/abs/1911.12129
Let $X$ be a complex projective manifold, $L$ an ample line bundle on $X$, and assume that we have a $\mathbb{C}^*$ action on $(X,L)$. We classify such triples $(X,L,\mathbb{C}^*)$ for which the closure of a general orbit of the $\mathbb{C}^*$ action
Externí odkaz:
http://arxiv.org/abs/1904.01896
We prove the LeBrun-Salamon Conjecture in low dimensions. More precisely, we show that a contact Fano manifold X of dimension 2n+1 that has reductive automorphism group of rank at least n-2 is necessarily homogeneous. This implies that any positive q
Externí odkaz:
http://arxiv.org/abs/1802.05002
We prove that the variety of complete flags for any semisimple algebraic group is rigid in any smooth family of Fano manifolds.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/1606.02670