On the Asymptotic Behavior of GW-Invariants and Some Recursively Defined Sequences

نویسنده

  • Aleksey Zinger
چکیده

The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants and of some recursively defined sequences. The speculations concerning the former may be indicative of some deep phenomena in symplectic topology that are outside of the reach of current techniques. The speculations concerning the latter appear in the style of some long established statements in algebraic combinatorics and analytic number theory.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Splice Graphs and their Vertex-Degree-Based Invariants

Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

متن کامل

Counting Curves in Elliptic Surfaces by Symplectic Methods

We explicitly compute family GW invariants of elliptic surfaces for primitive classes. That involves establishing a TRR formula and a symplectic sum formula for elliptic surfaces and then determining the GW invariants using an argument from [IP3]. In particular, as in [BL1], these calculations also confirm the well-known Yau-Zaslow Conjecture [YZ] for primitive classes in K3 surfaces. In [L] we...

متن کامل

Asymptotics of Some Convolutional Recurrences

We study the asymptotic behavior of the terms in sequences satisfying recurrences of the form an = an−1 + n−d k=d f(n, k)akan−k where, very roughly speaking, f(n, k) behaves like a product of reciprocals of binomial coefficients. Some examples of such sequences from map enumerations, Airy constants, and Painlevé I equations are discussed in detail. 1 Main results There are many examples in the ...

متن کامل

0 The Symplectic Sum Formula for Gromov - Witten Invariants

In the symplectic category there is a ‘connect sum’ operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum Z = X#Y in terms of the relative GW invariants ofX and Y . Several applications to enumerative geometry are given. Gromov-Witten invariants are co...

متن کامل

Oscillatory and Asymptotic Behavior of Fourth order Quasilinear Difference Equations

where ∆ is the forward difference operator defined by ∆xn = xn+1 −xn, α and β are positive constants, {pn} and {qn} are positive real sequences defined for all n ∈ N(n0) = {n0, n0 + 1, ...}, and n0 a nonnegative integer. By a solution of equation (1), we mean a real sequence {xn} that satisfies equation (1) for all n ∈ N(n0). If any four consecutive values of {xn} are given, then a solution {xn...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016