Results 11 to 20 of about 267 (34)

The Gromov width of complex Grassmannians [PDF]

, 2005
We show that the Gromov width of the Grassmannian of complex k-planes in C^n is equal to one when the symplectic form is normalized so that it generates the integral cohomology in degree 2. We deduce the lower bound from more general results. For example,
Biran, Delzant, Koszul, McDuff, Siebert, Susan Tolman, Traynor, Yael Karshon   +7 more
core   +3 more sources

HIGHER GENUS GROMOV–WITTEN THEORY OF $\mathsf{Hilb}^{n}(\mathbb{C}^{2})$ AND $\mathsf{CohFTs}$ ASSOCIATED TO LOCAL CURVES

Forum of Mathematics, Pi, 2019
We study the higher genus equivariant Gromov–Witten theory of the Hilbert scheme of $n$ points of $\mathbb{C}^{2}$. Since the equivariant quantum cohomology, computed by Okounkov and Pandharipande [Invent. Math.
RAHUL PANDHARIPANDE, HSIAN-HUA TSENG
doaj   +1 more source

Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure [PDF]

, 2016
We obtain a formula for the number of genus one curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface.
Biswas, Indranil, Mukherjee, Ritwik, Thakre, Varun   +2 more
core   +3 more sources

Differential and Functional Identities for the Elliptic Trilogarithm [PDF]

, 2009
When written in terms of $\vartheta$-functions, the classical Frobenius-Stickelberger pseudo-addition formula takes a very simple form. Generalizations of this functional identity are studied, where the functions involved are derivatives (including ...
Strachan, Ian A. B.
core   +4 more sources

Universal manifold pairings and positivity [PDF]

, 2005
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p= with values in (formal linear combinations of) closed manifolds.
Akbulut, Akbulut, Alexei Kitaev, Atiyah, Casson, Chetan Nayak, Freedman, Freedman, Johannes K Slingerland, Kevin Walker, Kirby, Kirby, Matveyev, Michael H Freedman, Schubert, Zhenghan Wang   +15 more
core   +9 more sources

Generalized Legendre transformations and symmetries of the WDVV equations [PDF]

, 2016
The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class - the so-called Legendre transformations - were introduced by Dubrovin.
Stedman, Richard, Strachan, Ian A. B.
core   +2 more sources

Minimal symplectic atlases of Hermitian symmetric spaces [PDF]

, 2015
In this paper we compute the minimal number of Darboux chart needed to cover a Hermitian symmetric space of compact type in terms of the degree of their embeddings in $\mathbb{C} P^N$. The proof is based on the recent work of Y. B. Rudyak and F. Schlenk [
Mossa, Roberto, Placini, Giovanni
core   +1 more source

Logarithmic asymptotics of the genus zero Gromov-Witten invariants of the blown up plane

, 2005
We study the growth of the genus zero Gromov-Witten invariants GW_{nD} of the projective plane P^2_k blown up at k points (where D is a class in the second homology group of P^2_k).
Di Francesco, Eugenii Shustin, Greuel, Göttsche, Hofer, Ilia Itenberg, Kollár, Kontsevich, McDuff, McDuff, McDuff, Viatcheslav Kharlamov   +11 more
core   +6 more sources

Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes [PDF]

, 2012
The degree zero part of the quantum cohomology algebra of a smooth Fano toric symplectic manifold is determined by the superpotential function, W, of its moment polytope. In particular, this algebra is semisimple, i.e.
Alexander Givental, Benjamin Nill, Benjamin P. Mirabelli, D. McDuff, David Cox, Günter Ewald, J. Lagarias, K. Fukaya, M. Entov, Maksim Maydanskiy, Matthew Strom Borman, Michael Usher, Mikkel Obro, Robin Hartshorne, T. Delzant, W. Fulton, Wilhelm Ljunggren, William Fulton, Y. Eliashberg, Y. Ostrover, Yaron Ostrover   +20 more
core   +1 more source

Open WDVV equations and Frobenius structures for toric Calabi-Yau 3-folds

Forum of Mathematics, Sigma
Let X be a toric Calabi-Yau 3-fold and let $L\subset X$ be an Aganagic-Vafa outer brane. We prove two versions of open WDVV equations for the open Gromov-Witten theory of $(X,L)$ .
Song Yu, Zhengyu Zong
doaj   +1 more source