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pro vyhledávání: '"Chen, Xujia"'
Autor:
Chen, Xujia, Zinger, Aleksey
We describe a sequence of smooth quotients of the Deligne-Mumford moduli space ${\mathbb R}\overline{\mathcal M}_{0,\ell+1}$ of real rational curves with $\ell\!+\!1$ conjugate pairs of marked points that terminates at ${\mathbb R}\overline{\mathcal
Externí odkaz:
http://arxiv.org/abs/2305.08811
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 boundary divisors modulo the ideal generated by the obvious geometric rela
Externí odkaz:
http://arxiv.org/abs/2305.08798
Autor:
Chen, Xujia
Kontsevich's characteristic classes are invariants of framed smooth fiber bundles with homology sphere fibers. It was shown by Watanabe that they can be used to distinguish smooth $S^4$-bundles that are all trivial as topological fiber bundles. In th
Externí odkaz:
http://arxiv.org/abs/2302.03021
Autor:
Qin, Rong, Fan, Xirui, Ding, Rui, Qiu, Yadan, Chen, Xujia, Liu, Yanting, Lin, Minjuan, Wang, Hui
Publikováno v:
In Heliyon 15 May 2024 10(9)
Autor:
Chen, Xujia
Publikováno v:
International Mathematics Research Notices, Volume 2022, Issue 9, 7021-7055
Our previous paper describes a geometric translation of the construction of open Gromov-Witten invariants by J. Solomon and S. Tukachinsky from a perspective of $A_{\infty}$-algebras of differential forms. We now use this geometric perspective to sho
Externí odkaz:
http://arxiv.org/abs/1912.05437
Autor:
Chen, Xujia
Publikováno v:
Peking Mathematical Journal 5 (2022) 279-348
The 2016 papers of J. Solomon and S. Tukachinsky use bounding chains in Fukaya's $A_{\infty}$-algebras to define numerical disk counts relative to a Lagrangian under certain regularity assumptions on the moduli spaces of disks. We present a (self-con
Externí odkaz:
http://arxiv.org/abs/1912.04119
Autor:
Chen, Xujia, Zinger, Aleksey
The present, partly expository, monograph consists of three parts. The first part treats Spin- and Pin-structures from three different perspectives and shows them to be suitably equivalent. It also introduces an intrinsic perspective on the relative
Externí odkaz:
http://arxiv.org/abs/1905.11316
Autor:
Chen, Xujia, Zinger, Aleksey
Publikováno v:
Mathematische Annalen 379 (2021) 1231-1313
The first author's previous work established Solomon's WDVV-type relations for Welschinger's invariant curve counts in real symplectic fourfolds by lifting geometric relations over possibly unorientable morphisms. We apply her framework to obtain WDV
Externí odkaz:
http://arxiv.org/abs/1904.04254
Autor:
Chen, Xujia, Zinger, Aleksey
Publikováno v:
Kyoto J. Math. 61(2) (2021) 339-376
We first recall Solomon's relations for Welschinger's invariants counting real curves in real symplectic fourfolds, announced in \cite{Jake2} and established in \cite{RealWDVV}, and the WDVV-style relations for Welschinger's invariants counting real
Externí odkaz:
http://arxiv.org/abs/1809.08938
Autor:
Chen, Xujia
Publikováno v:
Geometric and Functional Analysis 32 (2022) 490-567
We establish two WDVV-style relations for the disk invariants of real symplectic fourfolds by implementing Georgieva's suggestion to lift homology relations from the Deligne-Mumford moduli spaces of stable real curves. This is accomplished by lifting
Externí odkaz:
http://arxiv.org/abs/1809.08919