29 citations · 52 across the 14 of their papers we have counts for
15 papers
A geometric approach to the density of rank-metric codes
Shamil Asgarli, Lian Duan, Nathan Kaplan +1
We study the asymptotic density of -point-free linear sections of geometrically irreducible projective varieties over finite fields. We then apply these results to ra…
Mirror symmetry for lattice-polarized abelian surfaces
Yu-Wei Fan, Kuan-Wen Lai
Inspired by the Dolgachev-Nikulin-Pinkham mirror symmetry for lattice-polarized K3 surfaces, we study its analogue for abelian surfaces. In this paper, we introduce lattice-polariz…
Fourier-Mukai numbers of K3 categories of very general special cubic fourfolds
Yu-Wei Fan, Kuan-Wen Lai
We give counting formulas for the number of Fourier-Mukai partners of the K3 category of a very general special cubic fourfold.
On the irrationality of moduli spaces of projective hyperkähler manifolds
Daniele Agostini, Ignacio Barros, Kuan-Wen Lai
The aim of this paper is to estimate the irrationality of moduli spaces of hyperkähler manifolds of types K3, Kum, OG6, and OG10. We prove that the degrees of irratio…
Categorical Nielsen realization problems for generic K3 surfaces
Yu-Wei Fan, Kuan-Wen Lai
For a complex projective K3 surface of Picard number one, we prove that every nontrivial finite subgroup of autoequivalences has order two and compute the number of conjugacy class…
Frobenius nonclassical hypersurfaces
Shamil Asgarli, Lian Duan, Kuan-Wen Lai
A smooth hypersurface over a finite field is called Frobenius nonclassical if the image of every geometric point under the -th Frobenius endomorphism remains in t…
On the irrationality of moduli spaces of K3 surfaces
Daniele Agostini, Ignacio Barros, Kuan-Wen Lai
We study how the degrees of irrationality of moduli spaces of polarized K3 surfaces grow with respect to the genus . We prove that the growth is bounded by a polynomial function…
Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces
Kuan-Wen Lai, Masahiro Nakahara
A collection of varieties satisfies uniform potential density if each of them contains a dense subset of rational points after extending its ground field by a bounded degree. In th…
Transverse linear subspaces to hypersurfaces over finite fields
Shamil Asgarli, Lian Duan, Kuan-Wen Lai
Ballico proved that a smooth projective variety of degree over a finite field of elements admits a smooth hyperplane section if . In this paper,…
New rational cubic fourfolds arising from Cremona transformations
Yu-Wei Fan, Kuan-Wen Lai
Are Fourier-Mukai equivalent cubic fourfolds birationally equivalent? We obtain an affirmative answer to this question for very general cubic fourfolds of discriminant 20, where we…
Decomposition of Lagrangian classes on K3 surfaces
Kuan-Wen Lai, Yu-Shen Lin, Luca Schaffler
We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in ter…
Bijective Cremona transformations of the plane
Shamil Asgarli, Kuan-Wen Lai, Masahiro Nakahara +1
We study the birational self-maps of the projective plane over finite fields that induce permutations on the set of rational points. As a main result, we prove that no odd permutat…
Transverse lines to surfaces over finite fields
Shamil Asgarli, Lian Duan, Kuan-Wen Lai
We prove that if is a smooth reflexive surface in defined over a finite field , then there exists an -line meeting transversely p…
Cremona transformations and derived equivalences of K3 surfaces
Brendan Hassett, Kuan-Wen Lai
We exhibit a Cremona transformation of such that the base loci of the map and its inverse are birational to K3 surfaces. The two K3 surfaces are derived equivalent but…
New cubic fourfolds with odd degree unirational parametrizations
Kuan-Wen Lai
We prove that the moduli space of cubic fourfolds contains a divisor whose general member has a unirational parametrization of degree 13. This resu…