论文标题
Duistermaat-Heckman公式和Chern-Schwartz-Macpherson课程
The Duistermaat-Heckman formula and Chern-Schwartz-MacPherson classes
论文作者
论文摘要
让M成为一个光滑的复杂的投影品种，带有Kählersymbledectic形式ω和圆环T的哈密顿动作，具有有限的许多固定点m^t。 Duistermaat-Heckman定理的一种标准形式给出了M的Duistermaat-Heckman测度DH_T（M，ω）作为锥锥的交替总和。总体方向由M的摩尔斯分解确定。 利用Victor Ginzburg的Chern-Schwartz-Macpherson课程的建设，我们表明这些单独的锥术本身可以解释为T^*M中周期的Duistermaat-Heckman量度。 （这与维克托·金茨堡（Viktor Ginzburg），吉列林（Guillemin）和卡申（Karshon）的符合性恢复方法具有类似的目标。）我们的方法还暗示了包括Brianchon-gram定理在内的公式的扩展。
Let M be a smooth complex projective variety, bearing a Kähler symplectic form ωand a Hamiltonian action of a torus T, with finitely many fixed points M^T. One standard form of the Duistermaat-Heckman theorem gives a formula for M's Duistermaat-Heckman measure DH_T(M,ω) as an alternating sum of projections of cones, with overall direction determined by a Morse decomposition of M. Using Victor Ginzburg's construction of Chern-Schwartz-MacPherson classes, we show that these individual cone terms can themselves be interpreted as Duistermaat-Heckman measures of cycles in T^*M. (This has a similar goal to the symplectic cobordism approach of Viktor Ginzburg, Guillemin, and Karshon.) Our approach also suggests extensions of the formula, including the Brianchon-Gram theorem.
