Related papers: Genus one enumerative invariants in P^n with fixed…

Let K be a complete discretely valued field with residue field k. If char(K) = 0, char(k) = 2 and the 2-rank of k is d, we prove that there exists an integer N depending on d such that the u-invariant of any function field in one variable…

Let $E$ be an elliptic curve over $Q$, and $\tau$ an Artin representation over $Q$ that factors through the non-abelian extension $Q(\sqrt[p^n]{m},\mu_{p^n})/Q$, where $p$ is an odd prime and $n,m$ are positive integers. We show that…

For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space…

Let X be a regular irreducible variety in CP^{n-1}, Y the associated homogeneous variety in C^n, and N the restriction of the universal bundle of CP^{n-1} to X. In the present paper, we compute the obstructions to solving the d-bar-equation…

The genus 0, fixed-domain log Gromov-Witten invariants of a smooth, projective toric variety X enumerate maps from a general pointed rational curve to a smooth, projective toric variety passing through the maximal number of general points…

The scope of the paper is threefold. First, we build on recent work by Hayden to compute Hedden's tau-invariant $\tau_{\xi}(L)$ in the case when $\xi$ is a Stein fillable contact structure on a rational homology sphere, and $L$ is a…

Let $(X,0)$ be the germ of an equidimensional analytic set in $(\mathbb C^n,0)$ and $f=(f_1,f_2)$ a map-germ into the plane defined on $X.$ In this work, we investigate topological invariants associated to the pair $(f,X),$ among them, the…

We introduce a geometric refinement of Gromov-Witten invariants for $\mathbb P^1$-bundles relative to the natural fiberwise boundary structure. We call these refined invariant correlated Gromov-Witten invariants. Furthermore, we prove a…

We continue our study of the local Gromov-Witten invariants of curves in Calabi-Yau 3-folds. We define relative invariants for the local theory which give rise to a 1+1-dimensional TQFT taking values in the ring Q[[t]]. The associated…

Construction of a universal finite-type invariant can be reduced, under suitable assumptions, to the solution of certain equations (the hexagon and pentagon equations) in a particular graded associative algebra of chord diagrams. An…

We investigate dynamical properties of the set of permutations of $\mathbb{Z}^d$ with restricted movement, i.e., permutations $\pi $ of $\mathbb{Z}^d$ such that $\pi (\mathbf{n})-\mathbf{n}$ lies, for every $\mathbf{n}\in \mathbb{Z}^d$, in…

Let $k$ be a field of characteristic 0, let $C/k$ be a uniquely trigonal genus 4 curve, and let $P \in C(k)$ be a simply ramified point of the uniquely trigonal morphism. We construct an assignment of an orbit of an algebraic group of type…

Let $\ell$ and $n$ be positive integers with $\ell$ prime. The modular curves $X_1(\ell^n)$ and $X_0(\ell^n)$ are algebraic curves over $\mathbb{Q}$ whose non-cuspidal points parameterize elliptic curves with a distinguished point of order…

We provide explicit bounds on the difference of heights of the $j$-invariants of isogenous elliptic curves defined over $\overline{\mathbb{Q}}$. The first one is reminiscent of a classical estimate for the Faltings height of isogenous…

For real toric surfaces and conjugation invariant point conditions with all conjugate pairs on the boundary divisors, we prove that the signed count of real curves of arbitrary genus in the linear system through the given points is…

Let d1 and d2 be discriminants of distinct quadratic imaginary orders O_d1 and O_d2 and let J(d1,d2) denote the product of differences of CM j-invariants with discriminants d1 and d2. In 1985, Gross and Zagier gave an elegant formula for…

A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established for graded (contractive) Hilbert modules over the complex polynomial algebra in d variables, d=1,2,3,....…

We prove that a rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least…

We consider the pull-back of a natural sequence of cohomology classes $\Theta_{g,n}\in H^{2(2g-2+n)}(\overline{\cal M}_{g,n})$ to the moduli space of stable maps ${\cal M}^g_n(\mathbb{P}^1,d)$. These classes are related to the…

Let $X\subset \mathbb P^r$ be a projective factorial variety of dimension $3$, degree $n$, with at worst isolated singularities. Assume that the Picard group of $X$ is generated by the hyperplane section class. Let $C\subset X$ be a…