Zobrazeno 1 - 10
of 187
pro vyhledávání: '"Satriano, Matthew"'
Autor:
Satriano, Matthew, Usatine, Jeremy
In a previous paper we showed that any variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. In this paper we prove the converse, thereby proving that a variety admits a crepant resolution by a smooth Artin stac
Externí odkaz:
http://arxiv.org/abs/2410.23951
We show that any good moduli space $\pi : \mathcal{X} \to Y$ has a splitting after a proper, generically finite covering of $Y$. As an application we generalize Koll\'ar's ampleness lemma to give a criterion for projectivity of a good moduli space.
Externí odkaz:
http://arxiv.org/abs/2408.11057
Soprunov and Soprunova introduced the notion of a good infinite family of toric codes. We prove that such good families do not exist by proving a more general Szemer\'edi-type result: for all $c\in(0,1]$ and all positive integers $N$, subsets of dens
Externí odkaz:
http://arxiv.org/abs/2406.00243
Determining the limiting behaviour of the Jacobian as the underlying curve degenerates has been the subject of much interest. For nodal singularities, there are beautiful constructions of Caporaso as well as Pandharipande of compactified universal Ja
Externí odkaz:
http://arxiv.org/abs/2405.05199
Let $X$ be a smooth projective algebraic variety over a number field $k$ and $P$ in $X(k)$. In 2007, the second author conjectured that, in a precise sense, if rational points on $X$ are dense enough, then the best rational approximations to $P$ must
Externí odkaz:
http://arxiv.org/abs/2403.02480
Gerstenhaber proved in 1961 that the unital algebra generated by a pair of commuting $d\times d$ matrices over a field has dimension at most $d$. It is an open problem whether the analogous statement is true for triples of matrices which pairwise com
Externí odkaz:
http://arxiv.org/abs/2402.16334
Autor:
Satriano, Matthew, Usatine, Jeremy
We introduce a natural generalization of twisted maps, called \emph{warped maps}. While twisted maps play an important role in the study of Deligne-Mumford stacks, warped maps are better suited for studying Artin stacks. Heuristically, warped maps se
Externí odkaz:
http://arxiv.org/abs/2309.11434
Autor:
Satriano, Matthew, Usatine, Jeremy
Let $\mathcal{X} \to Y$ be a birational modification of a variety by an Artin stack. In previous work, under the assumption that $\mathcal{X}$ is smooth, we proved a change of variables formula relating motivic integrals over arcs of $Y$ to motivic i
Externí odkaz:
http://arxiv.org/abs/2309.11442
Autor:
Monahan, Sean, Satriano, Matthew
Let $X$ be a smooth projective split horospherical variety over a number field $k$ and $x\in X(k)$. Contingent on Vojta's conjecture, we construct a curve $C$ through $x$ such that (in a precise sense) rational points on $C$ approximate $x$ better th
Externí odkaz:
http://arxiv.org/abs/2308.11847
Let $X$ be an algebraic variety equipped with a dominant rational self-map $\phi:X\to X$. A new quantity measuring the interaction of $(X,\phi)$ with trivial dynamical systems is introduced; the stabilised algebraic dimension of $(X,\phi)$ captures t
Externí odkaz:
http://arxiv.org/abs/2306.11108