There are some Calabi-Yau threefolds that do not contain any rational curves, e.g. Calabi-Yau threefold of type A in the paper "Calabi-Yau threefolds of quotient type" by Oguiso an …

Let $\pi :D \subset \mathcal{X} \to S$ be a flat family of stable curves of genus $g$ with marked points $D$. Let $\mathcal{X} \to X$ be a flat family of stable morphisms in the se …

I'm working on a project and I've used the Picard-Fuchs equation at a maximally unipotent monodromy point for a certain 1-dimensional family of Calabi-Yau 3-folds to calculate the …

For smooth Deligne-Mumford stacks, there is a well-defined Gromov-Witten theory, see http://arxiv.org/pdf/math/0103156.pdf and http://arxiv.org/pdf/math/0603151.pdf. Is there some …

I am learning about mirror symmetry and having trouble understanding Givental's I- and J-functions. For example the J-function for the quintic threefold $X$ is defined by the formu …

I am working on some basic of Gromov-Witten theory and stuck in understanding obstruction bundle. Recall that a perfect obstruction theory on a scheme or stack $M$ due to Behrend a …

Is it possible to setup classical cobordism theory in the context of orbifolds? For example, let's consider the free abelian group generated by oriented smooth orbifolds and quoti …

Why is GW invariants of K3 surfaces are trivial? My naive guess is that GW invariants are deformation invariant and you can always deform your K3 surface to non-projective one, whi …

I am studying GW theory (and DT theory) in algebraic geometry. I now understand the heuristic "Aut, Def, Obs" argument written in Mirror Symmetry book (by Hori et al.), but it is t …

After studying some foundation of Gromow-Witten invariants, I now would like to see an explicit computation. I heard that one should first take a look at the total space of $\mathc …

Hello, I apologize in advance if this question is misguided somehow, since my algebraic geometry is pretty shaky. I am wondering if there is a way to understand all the conics in …

There is a famous recursion formula by Kontsevich to find the number of genus zero degree $d$ curves in $\mathbb{CP}^2$ through $3d-1$ points. My question is the following: Let $ …

Let $\mathscr{X}$ be a smooth DM-stack with projective coarse moduli space. I am interested in the orbifold cohomology ring $H^\mathrm{orb}(\mathscr{X})$, as defined by Chen-Ruan ( …

Let $X$ be a nonsingular projective 3-fold. I am trying to understand the proof of the GW/DT correspondence as presented in Gromov-Witten/Donaldson-Thomas correspondence for toric …

Let's consider closed simply-connected 4-manifold $M$ and some $a\in H^2(M)$. It is very natural question to estimate minimal $g$ that $a$ can be presented as embedded surface of g …