Results 1 to 10 of about 267 (35)
Multiple quantum products in toric varieties
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 11, Page 675-686, 2002., 2001 We generalize the author's formula for Gromov-Witten invariants of symplectic toric manifolds (see math.AG/0006156) to those needed to compute the quantum product of more than two classes directly, i.e.
Spielberg, Holger
core +6 more sources
The local motivic DT/PT correspondence
Journal of the London Mathematical Society, Volume 104, Issue 3, Page 1384-1432, October 2021., 2021 Abstract We show that the Quot scheme QLn=QuotA3(IL,n) parameterising length n quotients of the ideal sheaf of a line in A3 is a global critical locus, and calculate the resulting motivic partition function (varying n), in the ring of relative motives over the configuration space of points in A3.
Ben Davison, Andrea T. Ricolfi
wiley +1 more source
F‐Manifolds and geometry of information
Bulletin of the London Mathematical Society, Volume 52, Issue 5, Page 777-792, October 2020., 2020 Abstract The theory of F‐manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since the 1990s. The focus of this paper consists in the demonstration that various
Noémie Combe, Yuri I. Manin
wiley +1 more source
Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 954-1032, October 2020., 2020 Abstract I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the representation ring of E8 for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of ...
Andrea Brini
wiley +1 more source
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 +7 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
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 +2 more
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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 +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
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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