arXiv subjects

Xun Yu

Publications and source records attributed to Xun Yu.

25 records · Page 2Linked to original sources

arXiv2018

Classification of full exceptional collections of line bundles on three blow-ups of $\mathbb{P}^{3}$

A fullness conjecture of Kuznetsov says that if a smooth projective variety $X$ admits a full exceptional collection of line bundles of length $l$, then any exceptional collection of line bundles of length $l$ is full. In this paper, we show that this conjecture holds for $X$ as the blow-up of $\mathbb{P}^{3}$ at a point, a line, or a twisted cubic curve, i.e. any exceptional collection of line bundles of length 6 on $X$ is full. Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such $X$.

math.AG↗

arXiv2016

Elliptic fibrations on K3 surfaces and Salem numbers of maximal degree

We study the maximal Salem degree of automorphisms of K3 surfaces via elliptic fibrations. By generalizing \cite{EOY14}, we establish a characterization of such maximum in terms of elliptic fibrations with infinite automorphism groups. As an application, we show that any supersingular K3 surface in odd characteristic has an automorphism the entropy of which is the natural logarithm of a Salem number of degree $22$.

math.AG↗

arXiv2015

McKay correspondence and new Calabi-Yau threefolds

In this note, we consider crepant resolutions of the quotient varieties of smooth quintic threefolds by Gorenstein group actions. We compute their Hodge numbers via McKay correspondence. In this way, we find some new pairs $(h^{1,1},\;h^{2,1})$ of Hodge numbers of Calabi-Yau threefolds.

math.AG↗

arXiv2015

Automorphism groups of smooth quintic threefolds

We study automorphism groups of smooth quintic threefolds. Especially, we describe all the maximal ones with explicit examples of target quintic threefolds. There are exactly $22$ such groups.

math.AG↗

arXiv2014

Automorphisms of elliptic $K3$ surfaces and Salem numbers of maximal degree

Using elliptic structures, we show that any supersingular K3 surface of Artin invariant $1$ in characteristic $p \not= 5$, $7$, $13$ has an automorphism the entropy of which is the natural logarithm of a Salem number of degree $22$.

math.AG↗

arXiv2013

On Castelnuovo theory and non-existence of smooth isolated curves in quintic threefolds

We give some necessary conditions for a smooth irreducible curve $C\subset \mathbb{P}^4$ to be isolated in a smooth quintic threefold, and also find a lower bound for $h^1(\mathcal{N}_{C/{\mathbb{P}^4}})$. Combining these with beautiful results in Castelnuovo theory, we prove certain non-existence results on smooth curves in smooth quintic threefolds. As an application, we can prove Knutsen's list of examples of smooth isolated curves in general quintic threefolds is complete up to degree 9.

math.AG↗

arXiv2012

On smooth and isolated curves in general complete intersection Calabi-Yau threefolds

Recently Knutsen found criteria for the curves in a complete linear system $|\mathcal{L}|$ on a smooth surface $X$ in a nodal K-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. In this article we develop new methods to check whether the set of nodes of $Y_0$ imposes independent conditions on $|\mathcal{L}|$. As an application, we find new smooth isolated curves in complete intersection Calabi-Yau threefolds.

math.AG↗