发帖
雷达卡
摘要翻译：
本文在前人的基础上，引入了闭实辛四维流形的变形不变量$chi^d_r$，$d\，$r\in\n$，这些不变量在实枚举几何中产生了下界，在H_2(X；\z)$，$r\in\n$中产生了变形不变量$(X,\omega,c_X)$。本文用辛场论的方法证明了当流形的实轨迹包含球面、环面或实射影平面时，下界是尖锐的（在最后一种情况下，在更强的假设下）。我们还证明了当r不太大时，当实轨迹包含球面或实射影平面时，二次幂除$\chi^d_r$（在最后一种情况下，在同样强的假设下）。最后给出了射影平面和二次椭球曲面的显式计算，以及得到它们的一般公式，这些公式包含了我们首先定义的一些相对不变量。
---
英文标题：
《Optimalit\'e, congruences et calculs d'invariants des vari\'et\'es
symplectiques r\'eelles de dimension quatre》
---
作者：
Jean-Yves Welschinger
---
最新提交年份：
2007
---
分类信息：
一级分类：Mathematics 数学
二级分类：Symplectic Geometry 辛几何
分类描述：Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统，辛流，经典可积系统
--
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
---
英文摘要：
This paper follows a previous one in which were introduced deformation invariants $\chi^d_r$, $d \in H_2 (X ; \Z)$, $r \in \N$, of closed real symplectic four-manifolds $(X, \omega, c_X)$, invariants which produced lower bounds in real enumerative geometry. We prove here using methods of symplectic field theory that the lower bounds are sharp when $r \leq 1$ and the real locus of the manifold contains a sphere, torus or real projective plane (under stronger assumptions in this last case). We also prove that a big power of two divides $\chi^d_r$ as soon as r is not too big and when the real locus contains a sphere or real projective plane (under the same stronger assumptions in this last case). We finally present some explicit computations in the case of the projective plane or quadric ellipsoid surface as well as the general formulas used to get them, formulas which involve some relative invariants that we first define.
---
PDF链接：
https://arxiv.org/pdf/0707.4317
京公网安备 11010802022788号
