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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...
Given the fundamental importance of moduli spaces and their applications in many different topics, we are organizing a week long conference titled "Moduli spaces and applications in geometry, topology...
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relationwith GromovWitten theory and integrable systems
We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable pointed curves van...
We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable pointed curves van...
The moduli spaces of trigonal curves are proven to be rational when the genus is divisible by 4.
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...
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 ...
Abstract: In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerb...
Abstract: We give an introduction to the compactification of the moduli space of surfaces of general type introduced by Koll\'ar and Shepherd-Barron and generalized to the case of surfaces with a divi...
Abstract: The basic object of the paper is the moduli space $M_{2,3}(L)$ of a closed polygonal linkage either in $\mathbb{R}^2$ or in $\mathbb{R}^3$. As was originally suggested by G. Khimshiashvili, ...

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