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6 papers · 2 filters
On higher syzygies of ruled surfaces II
Euisung Park
In this article we we continue the study of property of irrational ruled surfaces begun in \cite{ES}. Let be a ruled surface over a curve of genus with a minim…
A bound on the number of curves of a given degree through a general point of a projective variety
Jun-Muk Hwang
Let be an irreducible projective variety of dimension in a projective space and let be a point of . Denote by the space of curves of degree …
On the volumes of complex hyperbolic manifolds with cusps
Jun-Muk Hwang
We study the problem of bounding the number of cusps of a complex hyperbolic manifold in terms of its volume. Applying algebro-geometric methods using Mumford's work on toroidal co…
Rigidity of surjective holomorphic maps to Calabi-Yau manifolds
Jun-Muk Hwang
We prove that the space of surjective holomorphic maps from a compact complex manifold to a compact Kähler manifold with trivial canonical class and finite fundamental group is dis…
Gromov-Witten Invariants for Abelian and Nonabelian Quotients
Aaron Bertram, Ionut Ciocan-Fontanine, Bumsig Kim
We make precise conjectures relating the genus zero Gromov-Witten theory of a nonabelian GIT quotient X//G to that of the associated abelian quotient X//T by a maximal torus T in G…
Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic
Igor Dolgachev, JongHae Keum
We show that Mukai's classification of finite groups which may act symplectically on a complex K3 surface extends to positive characteristic under the assumptions that (i) the…