Results 21 to 30 of about 288 (46)
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
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
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 +20 more
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Frobenius 3-Folds via Singular Flat 3-Webs [PDF]
, 2012 We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ satisfying the following conditions: 1) the web germ ...
Agafonov, Sergey I.
core +5 more sources
Open WDVV equations and Frobenius structures for toric Calabi-Yau 3-folds
Forum of Mathematics, SigmaLet 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
, 2006 We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of ...
B. Dubrovin, O. I. Mokhov, O. I. Mokhov
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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
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A mirror theorem for Gromov-Witten theory without convexity
Forum of Mathematics, SigmaWe prove a genus zero Givental-style mirror theorem for all complete intersections in toric Deligne-Mumford stacks, which provides an explicit slice called big I-function on Givental’s Lagrangian cone for such targets.
Jun Wang
doaj +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 +11 more
core +6 more sources
Frobenius manifolds and Frobenius algebra-valued integrable systems [PDF]
, 2017 The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved ...
Strachan, Ian A.B., Zuo, Dafeng
core +1 more source