jaxvacua.conifold.coni.Conifold

jaxvacua.conifold.coni.Conifold#

class Conifold(*, ncf=0, conifold_curve=None, conifold_curve0=None, basis_change=None, flop_edge=None, one_face_divisors=None, polytope=None, dual_triangulation=None, bulk_embedding=None, bulk_projection=None, embedding=None)#

Bases: object

Represents a conifold singularity in complex structure moduli space dual to a flop transition in Kähler moduli space.

Details

A conifold singularity appears at the boundary of complex structure moduli space where a rational curve in the mirror Calabi-Yau shrinks to zero size. On the mirror side, this corresponds to a topological transition — a flop — in Kähler moduli space.

The flop is encoded in the triangulation of the toric polytope: a specific edge inside a 2-face of the dual polytope can be flipped (Whitehouse flip), and the corresponding curve is an extremal generator of the Mori cone. The class stores the data needed to characterise this transition:

Flop edge \(e\) — the edge in the dual triangulation that undergoes the flip.
One-face divisors — divisor indices interior to the 1-face of the polytope dual to the conifold (these become light in the coniLCS limit).
Gopakumar-Vafa invariant \(n_{\rm cf}\) — the genus-0 GV invariant of the flopping curve.
Conifold curve \(q \in \mathbb{Z}^{h^{1,1}}\) (original-basis charge) and conifold_curve0 = \(q\,\Lambda^{T} = (1,0,\ldots,0)\) (canonical-basis charge after the basis transformation \(\Lambda\)); both are eagerly materialised at construction in geometric mode.

The class supports two construction modes via the from_geometry() and from_data() classmethods. After a JAX pytree round-trip, the cytools refs (polytope(), dual_triangulation()) return None; the numerical state survives unchanged.

__init__(*, ncf=0, conifold_curve=None, conifold_curve0=None, basis_change=None, flop_edge=None, one_face_divisors=None, polytope=None, dual_triangulation=None, bulk_embedding=None, bulk_projection=None, embedding=None)#: Low-level keyword-only constructor; prefer from_geometry() or from_data() in user code.

Methods

`__init__`(*[, ncf, conifold_curve, ...])	Low-level keyword-only constructor; prefer `from_geometry()` or `from_data()` in user code.
`basis_change`()	Returns the unimodular basis change matrix \(\Lambda\) that maps the `conifold_curve` to \((1, 0, \ldots, 0)\). Computed lazily on first call when the cache is empty and a `conifold_curve` is available.
`dual_triangulation`()	Returns the cytools fine, regular, star triangulation of the dual polytope, or `None` after a JAX pytree round-trip.
`flop_edge`()	Returns the pair of point indices forming the flop edge in the dual triangulation.
`from_data`(**kwargs)	Construct a numerical-only `Conifold` from kwargs. If `conifold_curve` and `basis_change` are supplied but `conifold_curve0` is omitted, it is derived as `conifold_curve @ basis_change.T`.
`from_geometry`(polytope, dual_triangulation, ...)	Construct a `Conifold` from cytools geometry. Eagerly computes `conifold_curve`, `conifold_curve0` and the basis-change matrix from the supplied polytope, triangulation and flop edge.
`one_face_divisors`([as_index])	Returns the divisors interior to the 1-face dual to the conifold transition.
`polytope`()	Returns the cytools polytope, or `None` after a JAX pytree round-trip (geometric data is dropped at the pytree boundary).
`to_data`()	Return a numerical-only copy of this `Conifold` suitable for carrying across a JAX pytree boundary. The cytools refs are stripped; the lazy basis-change cache is warmed first if a `conifold_curve` is available.

basis_change()#

Returns the unimodular basis change matrix \(\Lambda\) that maps the conifold_curve to \((1, 0, \ldots, 0)\). Computed lazily on first call when the cache is empty and a conifold_curve is available.

Returns:

Array | None – Integer matrix
:math:`Lambda in mathrm{GL} (h^{1,1},mathbb{Z})
:math:` (h^{1,1}, h^{1,1})
``conifold_curve`` is available.

jaxvacua.conifold.coni.Conifold

Contents

jaxvacua.conifold.coni.Conifold#