# Tagged Questions

**2**

votes

**2**answers

201 views

### Connections on the Hodge bundle?

Let $\mathcal{M}_g$ be the moduli space of curves of genus $g$. Consider the holomorphic bundle $\mathcal{H}^k\rightarrow\mathcal{M}_g$ whose fiber over a curve $C\in\mathcal{M}_g$ is the space of ...

**12**

votes

**3**answers

595 views

### What is the DGLA controlling the deformation theory of a complex submanifold?

Let $X$ be a complex manifold, $Y\hookrightarrow X$ a complex compact submanifold. Let $T_{X/Y}$ denote the normal bundle of $Y$ in $X$, and $\mathcal{O}(T_{X/Y})$ its sheaf of holomorphic sections. ...

**6**

votes

**2**answers

695 views

### Floer homology and Invariants for Einstein Field Equations?

Motivation: There have been the instanton (anti-self dual connection) solutions to the Yang-Mills equation $d_A^\ast F_A=0$ which extremize the YM energy $\int_M|F_A|^2$, leading to the Donaldson ...

**28**

votes

**2**answers

2k views

### Meaning/Origin of Seiberg-Witten Equations/Invariants

Having now seen and "understood" (quotes necessary) the Seiberg-Witten equations on a closed oriented Riemannian 4-manifold $X$, I have no real understanding of where they came from.
We take an ...

**5**

votes

**1**answer

549 views

### Flat Principal Connections and Homotopy Groups?

I've come across a comment in a paper that hints at a relation between the set of (flat) connections for a principal bundle and the homotopy group of the base of the bundle. Can anyone tell me what ...

**12**

votes

**1**answer

377 views

### What is the second fundamental form of moduli space?

Away from the hyperelliptic locus, the moduli of curves immerses
in the moduli of principally polarized abelian varieties. The
ambient space has a riemannian metric, so one can ask about the
second ...

**7**

votes

**0**answers

478 views

### Central Yang-Mills connections, and flat connections with prescribed holonomy

Let $X$ be $\Sigma^g$ which is the Riemann surface of genus $g$, and consider a trivial $G$-bundle over it.
1) In this $2$-d setting, the space of Yang-Mills central connections is the set of ...

**7**

votes

**1**answer

823 views

### Seiberg-Witten theory on 4-manifolds with boundary

What generalizations of Seiberg-Witten theory to 4-manifolds with boundary do exist?
I would be especially interested in theories which "behave good" under gluing along the boundary (comparable to ...

**19**

votes

**1**answer

861 views

### Do hyperKahler manifolds live in quaternionic-Kahler families?

A geometry question that I thought about more seriously a few years ago... thought it'd be a good first question for MO.
I'm aware that there are a number of Torelli type theorems now proven for ...

**6**

votes

**3**answers

500 views

### Geometric calculations using Grassmann variables

Physicists seem to get huge computational value by introducing Grassmann variables and Grassmann integration into differential geometric calculations.
See: ...