Real orientations, real Gromov-Witten theory, and real enumerative geometry
نویسندگان
چکیده
منابع مشابه
Real Orientations, Real Gromov-Witten Theory, and Real Enumerative Geometry
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 spaces and the renowned quintic threefold, its properties, and its connections with real enumerative geometry. Our construction introduces the principle of orienting the determinant of a differential operator relative to...
متن کاملReal Gromov-Witten Theory in All Genera and Real Enumerative Geometry: Properties
The first part of this work constructs positive-genus real Gromov-Witten invariants of realorientable symplectic manifolds of odd “complex” dimensions; the present part focuses on their properties that are essential for actually working with these invariants. We determine the compatibility of the orientations on the moduli spaces of real maps constructed in the first part with the standard node...
متن کاملReal Gromov-Witten Theory in All Genera and Real Enumerative Geometry: Construction
We construct positive-genus analogues of Welschinger’s invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for counts of real positive-genus curves in real algebraic varieties. Our approach to the orientability problem is based entirely on the topology of real bundle...
متن کاملReal Gromov-Witten Theory in All Genera and Real Enumerative Geometry: Computation
The first part of this work constructs positive-genus real Gromov-Witten invariants of realorientable symplectic manifolds of odd “complex” dimensions; the second part studies the orientations on the moduli spaces of real maps used in constructing these invariants. The present paper applies the results of the latter to obtain quantitative and qualitative conclusions about the invariants defined...
متن کاملOrientability in Real Gromov-Witten Theory
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 manifold which ensure that the uncompactified moduli spaces of real maps are orientable for all genera of and for all types of involutions on the domain. In contrast to the typical approaches to this problem, we do n...
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ژورنال
عنوان ژورنال: Electronic Research Announcements in Mathematical Sciences
سال: 2017
ISSN: 1935-9179
DOI: 10.3934/era.2017.24.010