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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Homological instability for the moduli space of smooth 4-manifolds
光滑 4-流形模空间 同调不稳定性
2023/5/5
The moduli space of a smooth manifold X is defined to be the classifying space of its diffeomorphism group. Understanding the cohomology group of this space is important because elements in this group...
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...
THE MODULI SPACE OF WEIGHTED CONFIGURA TIONS ON PROJECTIVE SPACE
MODULI SPACE WEIGHTED CONFIGURA TIONS PROJECTIVE SPACE
2015/10/14
THE MODULI SPACE OF WEIGHTED CONFIGURA TIONS ON PROJECTIVE SPACE.
ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE
MODULI SPACE POLYGONS EUCLIDEAN PLANE
2015/10/14
ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE.
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...
A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into P n
Genus-One Stable Maps Moduli
2015/7/14
We construct a natural smooth compacti cation of the space of smooth genus-one curves with
k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth
compacti ca...
THE MODULI SPACE OF CURVES, DOUBLE HURWITZ NUMBERS, AND FABER’S INTERSECTION NUMBER CONJECTURE
DOUBLE HURWITZ NUMBERS FABER’S INTERSECTION NUMBER CONJECTURE
2015/7/14
We define the dimension 2g − 1 Faber-Hurwitz Chow/homology classes on the moduli
space of curves, parametrizing curves expressible as branched covers of P
1 with given ramification...
The moduli space of curves has proven itself a central object in geometry. The past
decade has seen substantial progress in understanding the moduli space of curves, involving ideas, for example, fro...
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...
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 pr...
As an illustration, we describe a new approach to Faber’s intersection number
conjecture via branched covers of the projective line (work with I.P. Goulden and D.M.
Jackson, based on work with T. Gr...
Boundary Divisors in the Moduli Space of Stable Quintic Surfaces
algebraic geometry deformation theory moduli space
2014/12/8
I give a bound on which singularities may appear on KSBA stable surfaces for a wide range of topological invariants, and use this result to describe all stable numerical quintic surfaces, i.e. stable ...
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...
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'...
Dimension of the moduli space and Hamiltonian analysis of BF field theories
Index theorem moduli space Hamiltonian dynamics
2011/9/22
Abstract: By using the Atiyah-Singer theorem through some similarities with the instanton and the anti-instanton moduli spaces, the dimension of the moduli space for two and four-dimensional BF theori...