Real Gromov–Witten theory in all genera and real enumerative geometry: computation
نویسندگان
چکیده
منابع مشابه
Real 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 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 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 کاملEnumerative Real Algebraic Geometry
Two well-defined classes of structured polynomial systems have been studied from this point of view—sparse systems, where the structure is encoded by the monomials in the polynomials fi—and geometric systems, where the structure comes from geometry. This second class consists of polynomial formulations of enumerative geometric problems, and in this case Question 1.1 is the motivating question o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2019
ISSN: 0022-040X
DOI: 10.4310/jdg/1573786971