12 citations · 28 across the 13 of their papers we have counts for
13 papers
Asymptotic Betti bounds for hypersurfaces in a singular variety
Xuanyu Pan, Dingxin Zhang, Xiping Zhang
We show that for any degree hypersurface in a possibly singular projective variety , the total Betti number of is bounded by $3\text{d…
-Fold -Blocking Sets and -Minimal Codes
Hao Chen, Xu Pan, Conghui Xie
Blocking sets and minimal codes have been studied for many years in projective geometry and coding theory. In this paper, we provide a new lower bound on the size of -fold -b…
Logarithmic de Rham comparison for open rigid spaces
Shizhang Li, Xuanyu Pan
In this note, we prove the logarithmic -adic comparison theorem for open rigid analytic varieties. We prove that a smooth rigid analytic variety with a strict simple normal cros…
1-Cycles on Fano varieties
Cristian Minoccheri, Xuanyu Pan
We prove results about 1-cycles on certain Fano varieties using techniques that rely on rational curves. Firstly, we show that Fano weighted complete intersections with index bigge…
p-adic deformation of graph cycles
Xuanyu Pan
In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory…
2-Cycles on Higher Fano Hypersurfaces
Xuanyu Pan
Let F(X_d) be a smooth Fano variety of lines of a hypersurface X_d of degree d. In this paper, we prove the Griffiths group Griff_1(F(X_d)) is trivial if the hypersurface X_d is of…
Automorphism and Cohomology II: Complete intersections
Xi Chen, Xuanyu Pan, Dingxin Zhang
We prove that the automorphism group of a general complete intersection in a projective space is trivial with a few well-understood exceptions. We also prove that the automorph…
Automorphism and Cohomology I: Fano variety of lines and Cubic
Xuanyu Pan
In this paper, we prove a general principle of lifting an automorphism from positive characteristic to zero characteristic. We based on the principle to prove the automorphism grou…
Unobstructedness of deformations of Calabi-Yau varieties with a line bundle
Shizhang Li, Xuanyu Pan
We generalize the Tian-Todorov Theorem in the case of Calabi-Yau varieties equipped with a line bundle.
Triviality and Split of Vector Bundles on Rationally Connected Varieties
Xuanyu Pan
In this paper, we give a simple proof of a triviality criterion due to I.Biswas and J.Pedro and P.Dos Santos. We also prove a vector bundle on a homogenous space is trivial if and…
Geometry of Rational Curves on Low degree Complete Intersections
Xuanyu Pan
For a smooth complete intersection X, we consider a general fiber \mathbb{F} of the evaluation map ev of Kontsevich moduli space \bar{M}_{0,m}(X,m)\rightarrow X^m and the forgetful…
Spaces of conics on low degree complete intersections
Xuanyu Pan
Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smo…
Some examples on moduli spaces of low degree rational curves on low degree complete intersections
Xuanyu Pan
This paper is to give some concrete examples of the general fibers of the evaluation map of some Kontsevich mapping spaces parametrize low degree rational curves on low degree comp…