On the integrals over two-dimensional compact complex toric varieties

Olga S. Ulvert

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: In this paper, we proof that an integral of smooth $(2,2)$-form over two-dimensional compact complex toric variety $X$ (which contains complex torus $\mathbb T^2$) is equal to the integral of holomorphic $(2,0)$-form over real torus $T^2\subset\mathbb T^2$.

Keywords: differential form, toric variety, Dolbeault cohomology, Čech cohomology.

UDC: 515.171.6

Received: 18.05.2010
Received in revised form: 25.06.2010
Accepted: 10.07.2010

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