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In this talk, I will explain the relationship between the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces and the existence of Shokurov polytopes. For K3 fibrations, this enables us to e...
The topic for 2017 Tianyuan Spring School is: higher dimensional algebraic varieties and moduli theory, including biraitonal geometry, stability theory and the geometry of Fano varieties. The topics o...
The topic for 2017 Tianyuan Spring School is: higher dimensional algebraic varieties and moduli theory, including biraitonal geometry, stability theory and the geometry of Fano varieties. The topics o...
In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a ...
We consider the question: “How bad can the deformation space of an object be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as possible...
This paper lays the foundations for the global theory of irreducible components of rigid analytic spaces over a complete eld k. We prove the excellence of the local rings on rigid spaces over k. Thi...
The moduli spaces of trigonal curves are proven to be rational when the genus is divisible by 4.
This paper reviews results and techniques from the authors' previous work "Symplectomorphism group relations and degenerations of Landau-Ginzburg models" and applies them in basic examples. The main e...
We prove uniruledness of some moduli spaces $\bar{M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points using linear systems on nonsingular projective surfaces containing the general curve of...
We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a weak analog of the Keel-Mori theorem, which guarantees the existence of a coarse mo...
We show that the automorphism group of Drinfeld's half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the s...
A line bundle L on a smooth curve X is nonspecial if and only if L admits a presentation L=K_X -D +E for some effective divisors D and E>0 on X with gcd (D, E)=0 and h^0 (X, O_X (D))=1. In this work, ...
A symplectic or orthogonal bundle $V$ of rank $2n$ over a curve has an invariant $t(V)$ which measures the maximal degree of its isotropic subbundles of rank $n$. This invariant $t$ defines stratifica...
Abstract: In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with...
Abstract: We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques ...

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