88 research outputs found
Hori--Vafa mirror models for complete intersections in weighted projective spaces and weak Landau--Ginzburg models
We prove that Hori--Vafa mirror models for smooth Fano complete intersections
in weighted projective spaces admit an interpretation as Laurent polynomials.Comment: 5 pages; several minor changes has been mad
Gromov-Witten invariants of Fano threefolds of genera 6 and 8
The aim of this paper is to prove Golyshev's conjecture in the cases of Fano
threefolds and . This conjecture states modularity of D3
equations for smooth Fano threefolds with Picard group Z. More precisely, we
find counting matrices of prime two-pointed Gromov-Witten invariants for them.
For this we use the method that lets us find Gromov-Witten invariants of
complete intersections in varieties whose invariants are (partially) known.Comment: 12 pages, 1 figure, typos correcte
Minimal Gromov--Witten ring
We build the abstract theory of Gromov-Witten invariants of genus 0 for
quantum minimal Fano varieties (a minimal natural (with respect to
Gromov-Witten theory) class of varieties). In particular, we consider ``the
minimal Gromov-Witten ring'', i. e. a commutative algebra with generators and
relations of the form used in the Gromov-Witten theory of Fano variety (of
unspecified dimension). Gromov-Witten theory of any quantum minimal variety is
a homomorphism of this ring to . We prove the Abstract
Reconstruction Theorem which states the particular isomorphism of this ring
with a free commutative ring generated by ``prime two-pointed invariants''. We
also find the solutions of the differential equations of type DN for a Fano
variety of dimension N in terms of generating series of one-pointed
Gromov-Witten invariants.Comment: 14 page
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