19 citations · 52 across the 11 of their papers we have counts for
18 papers
Algebraic Properties of Real Gromov-Witten Invariants
Penka Georgieva, Aleksey Zinger
We describe properties of the previously constructed all-genus real Gromov-Witten theory in the style of Kontsevich-Manin's axioms and other classical equations and reconstruction…
Geometric Properties of Real Gromov-Witten Invariants
Penka Georgieva, Aleksey Zinger
We collect geometric properties of the all-genus real Gromov-Witten theory and provide updates on its development since its introduction in 2015. We bring attention to a modificati…
The Cohomology Ring of the Deligne-Mumford Moduli Space of Real Rational Curves with Conjugate Marked Points
Xujia Chen, Penka Georgieva, Aleksey Zinger
It is a long-established and heavily-used fact that the integral cohomology ring of the Deligne-Mumford moduli space of (complex) rational curves is the polynomial ring on the boun…
Splitting formulas for the local real Gromov-Witten invariants
Penka Georgieva, Eleny-Nicoleta Ionel
Motivated by the real version of the Gopakumar-Vafa conjecture for 3-folds, the authors introduced in [GI] the notion of local real Gromov-Witten invariants associated to local 3-f…
A Klein TQFT: the local Real Gromov-Witten theory of curves
Penka Georgieva, Eleny-Nicoleta Ionel
In this paper we study the Real Gromov-Witten theory of local 3-folds over Real curves. We show that this gives rise to a 2-dimensional Klein TQFT defined on an extension of the ca…
Real Orientations, Real Gromov-Witten Theory, and Real Enumerative Geometry
Penka Georgieva, Aleksey Zinger
The present note overviews our recent construction of real Gromov-Witten theory in arbitrary genera for many real symplectic manifolds, including the odd-dimensional projective spa…
On the Topology of Real Bundle Pairs over Nodal Symmetric Surfaces
Penka Georgieva, Aleksey Zinger
We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also class…
Real Gromov-Witten Theory in All Genera and Real Enumerative Geometry: Computation
Penka Georgieva, Aleksey Zinger
The first part of this work constructs real positive-genus Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the second part studies the…
Pencils of quadrics and Gromov-Witten-Welschinger invariants of
Erwan Brugalle, Penka Georgieva
We establish a formula for the Gromov-Witten-Welschinger invariants of with mixed real and conjugate point constraints. The method is based on a suggestion by J. Kol…
Real Gromov-Witten Theory in All Genera and Real Enumerative Geometry: Properties
Penka Georgieva, Aleksey Zinger
The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on…
Real Gromov-Witten Theory in All Genera and Real Enumerative Geometry: Construction
Penka Georgieva, Aleksey Zinger
We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic three…
A recursion for counts of real curves in CP^{2n-1}: another proof
Penka Georgieva, Aleksey Zinger
In a recent paper, we obtained a WDVV-type relation for real genus 0 Gromov-Witten invariants with conjugate pairs of insertions; it specializes to a complete recursion in the case…
Enumeration of real curves in CP^{2n-1} and a WDVV relation for real Gromov-Witten invariants
Penka Georgieva, Aleksey Zinger
We establish a homology relation for the Deligne-Mumford moduli spaces of real curves which lifts to a WDVV-type relation for real Gromov-Witten invariants of real symplectic manif…
Orientability in real Gromov-Witten theory
Penka Georgieva, Aleksey Zinger
The orientability problem in real Gromov-Witten theory is one of the fundamental hurdles to enumerating real curves. In this paper, we describe topological conditions on the target…
The moduli space of maps with crosscaps: the relative signs of the natural automorphisms
Penka Georgieva, Aleksey Zinger
Just as a symmetric surface with separating fixed locus halves into two oriented bordered surfaces, an arbitrary symmetric surface halves into two oriented symmetric half-surfaces,…
Open Gromov-Witten disk invariants in the presence of an anti-symplectic involution
Penka Georgieva
For a symplectic manifold with an anti-symplectic involution having non-empty fixed locus, we construct a model of the moduli space of real sphere maps out of moduli spaces of deco…
The moduli space of maps with crosscaps: Fredholm theory and orientability
Penka Georgieva, Aleksey Zinger
Just as a symmetric surface with separating fixed locus halves into two oriented bordered surfaces, an arbitrary symmetric surface halves into two oriented symmetric half-surfaces,…
The orientability problem in open Gromov-Witten theory
Penka Georgieva
We give an explicit formula for the holonomy of the orientation bundle of a family of real Cauchy-Riemann operators. A special case of this formula resolves the orientability quest…