34 citations · 150 across the 29 of their papers we have counts for
20 papers · 1 filter
Isotrivial smooth curves on surfaces
Xi Chen, Frank Gounelas
We prove that a smooth projective non-uniruled surface of Picard rank one, generated by an ample and base point free line bundle, cannot be covered by an isotrivial family of smoot…
When is the diagonal contractible?
Xi Chen, Frank Gounelas
For a smooth projective complex variety , we study the problem of when there exists a birational morphism to a projective variety contracting the diagonal $…
Trigonal Canonically Fibered Surfaces
Houari Benammar Ammar, Xi Chen, Nathan Grieve
We fix some gaps of a proof of Xiao's conjecture on canonically fibered surfaces of relative genus 5 by the second author. Our argument simplifies the original proof and gives a mu…
Severi Varieties on Ruled Surfaces over Elliptic Curves
Xiaotian Chang, Xi Chen, Adrian Zahariuc
We proved that the general members of Severi varieties on an Atiyah ruled surface over a general elliptic curve have nodes and ordinary triple points as singularities.
Curves of maximal moduli on K3 surfaces
Xi Chen, Frank Gounelas
We prove that if is a complex projective K3 surface and , then there exist infinitely many families of curves of geometric genus on with maximal, i.e., -dimensi…
Rational curves on lattice-polarised K3 surfaces
Xi Chen, Frank Gounelas, Christian Liedtke
Fix a K3 lattice of rank two and a big and nef divisor that is positive enough. We prove that the generic -polarised K3 surface has an integral nodal rational curve…