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“代数几何中的模空间”天元高级研讨会（Tianyuan Advanced Seminar on the Moduli Spaces in Algebraic Geometry）
代数几何中的模空间 天元 高级研讨会
2017/3/8
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...
Tianyuan Advanced Seminar on the Moduli Spaces in Algebraic Geometry
Tianyuan Advanced Seminar the Moduli Spaces in Algebraic Geometry
2017/2/15
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 EQUATIONS FOR THE MODULI SPACE OF n POINTS ON THE LINE
MODULI SPACE n POINTS ON THE LINE
2015/10/14
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural proj...
AN ANALYTIC CONSTRUCTION OF THE DELIGNE-MUMFORD COMPACTIFICATION OF THE MODULI SPACE OF CURVES
ANALYTIC CONSTRUCTION DELIGNE-MUMFORD COMPACTIFICATION MODULI SPACE OF CURVES
2015/8/26
In 1969, P. Deligne and D. Mumford compactified the modulispace of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alt...
THE AFFINE STRATIFICATION NUMBER AND THE MODULI SPACE OF CURVES
AFFINE STRATIFICATION NUMBER MODULI SPACE
2015/7/14
One relevant example (Example 4.9) turns out to be a proper integral variety with no
embeddings in a smooth algebraic space. This one-paragraph construction appears to be
simpler and more elementary...
The rationality of the moduli spaces of trigonal curves
trigonal curve rationality SL2 × SL2 bi-transvectant
2012/7/11
The moduli spaces of trigonal curves are proven to be rational when the genus is divisible by 4.
Uniruledness of some moduli spaces of stable pointed curves
Pointed curve Moduli space Uniruledness Hyperelliptic curves Complete intersection surfaces
2012/6/27
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...
Existence of good moduli spaces for A_k-stable curves
Existence of good moduli spaces A_k-stable curves Algebraic Geometry
2012/6/25
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...
Moduli of products of stable varieties
2012/6/18
We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined m...
Singularities of the moduli space of level curves
Singularities moduli space of level curves Algebraic Geometry
2012/5/9
For a fixed integer l>1, we describe the singular locus of the compactification of the moduli space R_{g,l} of curves of genus g paired with an l-torsion point in their Jacobian. Generalizing previous...
A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve
stratification moduli spaces symplectic orthogonal bundles curve Algebraic Geometry
2012/4/23
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...
Torelli theorem for the Deligne--Hitchin moduli space, II
Principal bundle Deligne–Hitchin moduli space Higgs bundle vector field
2012/3/1
Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components $M_{DH}^d(X,G)$ and $M_{DH}^{d'}(X'...
Beauville surfaces, moduli spaces and finite groups
Beauville surfaces moduli spaces finite groups Algebraic Geometry
2011/9/22
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...
Rank One Bridgeland Stable Moduli Spaces on A Principally Polarized Abelian Surface
Moduli space Hilbert scheme abelian surface Bridgeland stability wall crossing projectivity
2011/9/21
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: 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...