Zobrazeno 1 - 10
of 132
pro vyhledávání: '"de Fernex, Tommaso"'
Autor:
de Fernex, Tommaso, Wang, Shih-Hsin
Families of jets through singularities of algebraic varieties are here studied in relation to the families of arcs originally studied by Nash. After proving a general result relating them, we look at normal locally complete intersection varieties wit
Externí odkaz:
http://arxiv.org/abs/2306.08291
Given a morphism $f \colon X \to Y$ of schemes over a field, we prove several finiteness results about the fibers of the induced map on arc spaces $f_\infty \colon X_\infty \to Y_\infty$. Assuming that $f$ is quasi-finite and $X$ is separated and qua
Externí odkaz:
http://arxiv.org/abs/2206.08060
Autor:
de Fernex, Tommaso
Extending previous results, we prove that for $n \ge 5$ all hypersurfaces of degree $n+1$ in ${\mathbb P}^{n+1}$ with isolated ordinary double points are birational superrigid and K-stable, hence admit a weak K\"ahler--Einstein metric.
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Externí odkaz:
http://arxiv.org/abs/2111.09911
Autor:
de Fernex, Tommaso, Lau, Chung Ching
We define a motivic measure on the Berkovich analytification of an algebraic variety defined over a trivially valued field, and introduce motivic integration in this setting. The construction is geometric with a similar spirit as Kontsevich's origina
Externí odkaz:
http://arxiv.org/abs/2103.01811
Autor:
de Fernex, Tommaso, Lau, Chung Ching
Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration with rationally connected fibers. We apply this resul
Externí odkaz:
http://arxiv.org/abs/2011.10567
Publikováno v:
Forum Math. Pi 10 (2022), Paper No. e4, 37 pp
We introduce a notion of embedding codimension of an arbitrary local ring, establish some general properties, and study in detail the case of arc spaces of schemes of finite type over a field. Viewing the embedding codimension as a measure of singula
Externí odkaz:
http://arxiv.org/abs/2001.08377
Autor:
de Fernex, Tommaso, Lau, Chung Ching
We establish a Grothendieck--Lefschetz theorem for smooth ample subvarieties of smooth projective varieties over an algebraically closed field of characteristic zero and, more generally, for smooth subvarieties whose complement has small cohomologica
Externí odkaz:
http://arxiv.org/abs/1911.10385
Autor:
de Fernex, Tommaso
Building on work of Du, Gao, and Yau, we give a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi--Yau CR manifolds of dimension $2n-1 \ge 5$ and in the hypersurface case when $
Externí odkaz:
http://arxiv.org/abs/1801.00503
Autor:
de Fernex, Tommaso, Docampo, Roi
Publikováno v:
Ann. Inst. Fourier (Grenoble) 69 (2019), no. 6, 2577-2588
Given an arbitrary projective birational morphism of varieties, we provide a natural and explicit way of constructing relative compactifications of the maps induced on the main components of the jet schemes. In the case the morphism is the Nash blow-
Externí odkaz:
http://arxiv.org/abs/1712.00911
If a morphism of germs of schemes induces isomorphisms of all local jet schemes, does it follow that the morphism is an isomorphism? This problem is called the local isomorphism problem. In this paper, we use jet schemes to introduce various closure
Externí odkaz:
http://arxiv.org/abs/1704.07494