Gromov-witten Invariants of P1 and Eynard-orantin Invariants

نویسندگان

  • PAUL NORBURY
  • NICK SCOTT
چکیده

We prove that stationary Gromov-Witten invariants of P1 arise as the Eynard-Orantin invariants of the spectral curve x = z + 1/z, y = ln z. As an application we show that tautological intersection numbers on the moduli space of curves arise in the asymptotics of large degree Gromov-Witten invariants of P1.

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

Polynomials Representing Eynard-orantin Invariants

The Eynard-Orantin invariants of a plane curve are multilinear differentials on the curve. For a particular class of genus zero plane curves these invariants can be equivalently expressed in terms of simpler expressions given by polynomials obtained from an expansion of the Eynard-Orantin invariants around a point on the curve. This class of curves contains many interesting examples.

متن کامل

String and Dilaton Equations for Counting Lattice Points in the Moduli Space of Curves

We prove that the Eynard-Orantin symplectic invariants of the curve xy − y2 = 1 are the orbifold Euler characteristics of the moduli spaces of genus g curves. We do this by associating to the Eynard-Orantin invariants of xy − y2 = 1 a problem of enumerating covers of the two-sphere branched over three points. This viewpoint produces new recursion relations—string and dilaton equations—between t...

متن کامل

The Local Gromov–Witten Invariants of Configurations of Rational Curves

We compute the local Gromov–Witten invariants of certain configurations of rational curves in a Calabi–Yau threefold. These configurations are connected subcurves of the “minimal trivalent configuration”, which is a particular tree of P1 ’s with specified formal neighborhood. We show that these local invariants are equal to certain global or ordinary Gromov–Witten invariants of a blowup of P3 a...

متن کامل

Hilbert scheme intersection numbers , Hurwitz numbers , and Gromov - Witten invariants

Some connections of the ordinary intersection numbers of the Hilbert scheme of points on surfaces to the Hurwitz numbers for P1 as well as to the relative Gromov-Witten invariants of P1 are established.

متن کامل

All orders asymptotic expansion of large partitions

The generating function which counts partitions with the Plancherel measure (and its q-deformed version), can be rewritten as a matrix integral, which allows to compute its asymptotic expansion to all orders. There are applications in statistical physics of growing/melting crystals, T.A.S.E.P., and also in algebraic geometry. In particular we compute the Gromov-Witten invariants of the Xp = O(p...

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 2011