Eugene Z. Xia

activity

19992004

collaborators

11 papers

math.AG2004

Non-abelian Local Invariant Cycles

Yen-lung Tsai, Eugene Z. Xia

Let f be a degeneration of Kahler manifolds. The local invariant cycle theorem states that for a smooth fiber of the degeneration, any cohomology class, invariant under the monodro…

math.DS2003

Dynamics of the mapping class group on the moduli of a punctured sphere with rational holonomy

Joseph P. Previte, Eugene Z. Xia

Let $M$ be a four-holed sphere and $Γ$ the mapping class group of $M$ fixing the boundary $\partial M$ . The group $Γ$ acts on $M_{B} (S L (2, C)) = H o m_{B}^{+} (p i_{1} (M), S L (2, C)) / S L (2, C)$ whic…

math.AG2001

Frobenius pull-back and stability of vector bundles in characteristic 2

Jiu-Kang Yu, Eugene Z. Xia

Let X be a smooth projective curve of genus g>1 over an algebraically closed field of characteristic 2. Pull-back by the (absolute) Frobenius on X only defines a rational morphism…

math.DS2001

Exceptional Discrete Mapping Class Group Orbits in Moduli Spaces

Joseph P. Previte, Eugene Z. Xia

Let $M$ be a four-holed sphere and $Γ$ the mapping class group of $M$ fixing $\partial M$ . The group $Γ$ acts on the space $M_{B} (S U (2))$ of SU(2)-gauge equival…

math.AG2000

The Moduli of Flat PU(p,p)-Structures with Large Toledo Invariants

Eyal Markman, Eugene Z. Xia

For a compact Riemann surface $X$ of genus $g > 1$ , $\Hom(π_1(X), PU(p,q))/PU(p,q)$ is the moduli space of flat $P U (p, q)$ -connections on $X$ . There are two invariants, the Chern cl…

math.DS2000

Ergodicity of Mapping Class Group Actions on Representation Varieties, II. Surfaces with Boundary

Doug Pickrell, Eugene Z. Xia

The mapping class group of a compact oriented surface of genus greater than one with boundary acts ergodically on connected components of the representation variety corresponding t…