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pro vyhledávání: '"Cheng, Raymond"'
Autor:
Cheng, Raymond
The purpose of this note is to show that the minimal $e$ for which every smooth Fano hypersurface of dimension $n$ contains a free rational curve of degree at most $e$ cannot be bounded by a linear function in $n$ when the base field has positive cha
Externí odkaz:
http://arxiv.org/abs/2404.17341
We construct singular quartic double fivefolds whose Kuznetsov component admits a crepant categorical resolution of singularities by a twisted Calabi--Yau threefold. We also construct rational specializations of these fivefolds where such a resolutio
Externí odkaz:
http://arxiv.org/abs/2403.13463
Autor:
Cheng, Raymond
For any power $q$ of the positive ground field characteristic, a smooth $q$-bic threefold -- the Fermat threefold of degree $q+1$ for example -- has a smooth surface $S$ of lines which behaves like the Fano surface of a smooth cubic threefold. I deve
Externí odkaz:
http://arxiv.org/abs/2402.09884
Learning methods in Banach spaces are often formulated as regularization problems which minimize the sum of a data fidelity term in a Banach norm and a regularization term in another Banach norm. Due to the infinite dimensional nature of the space, s
Externí odkaz:
http://arxiv.org/abs/2312.05734
Autor:
Cheng, Raymond, Felder, Christopher
Publikováno v:
Pacific J. Math. 327 (2023) 267-295
This work studies optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, $H^p$ ($1 < p < \infty$). For fixed $f\in H^p$ and $n\in\mathbb{N}$, the OPA of degree $n$ associated to $f$ is the polynomial which minimizes th
Externí odkaz:
http://arxiv.org/abs/2310.16010
Autor:
Cheng, Raymond
A $q$-bic hypersurface is a hypersurface in projective space of degree $q+1$, where $q$ is a power of the positive ground field characteristic, whose equation consists of monomials which are products of a $q$-power and a linear power; the Fermat hype
Externí odkaz:
http://arxiv.org/abs/2307.06160
This work studies optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, $H^p$ ($1 < p < \infty$). In particular, we uncover some estimates concerning the OPAs of degree zero and one. It is also shown that if $f \in H^
Externí odkaz:
http://arxiv.org/abs/2305.16068
Autor:
Cheng, Raymond
A $q$-bic form is a pairing $V \times V \to \mathbf{k}$ that is linear in the second variable and $q$-power Frobenius linear in the first; here, $V$ is a vector space over a field $\mathbf{k}$ containing the finite field on $q^2$ elements. This artic
Externí odkaz:
http://arxiv.org/abs/2301.09929
Autor:
Cheng, Raymond
Traditional algebraic geometric invariants lose some of their potency in positive characteristic. For instance, smooth projective hypersurfaces may be covered by lines despite being of arbitrarily high degree. The purpose of this dissertation is to d
Autor:
Cheng, Raymond, Felder, Christopher
This work explores several aspects of interpolating sequences for $\ell^p_A$, the space of analytic functions on the unit disk with $p$-summable Maclaurin coefficients. Much of this work is communicated through a Carlesonian lens. We investigate vari
Externí odkaz:
http://arxiv.org/abs/2210.05823