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Online Talk

The singular cohomology ring of a smooth compact toric varietyÌýis given by a theorem of Danilov and Jurkiewicz. However, even the group structure of the integral cohomology is vastlyÌýunknown for singular compact toric varieties. Consider the Leray-Serre spectral sequence of the filtration by orbitÌýdimensions of the compact torus in a compact toric variety. It collapses at the second page for cellular cohomology with complexÌýcoefficients (by Danilov) and for rational Borel-Moore homology (byÌýTotaro). In the talk, a collapse result of this spectral sequence will be givenÌýfor singular cohomology with integral coefficients (with trivialÌýextension in abelian groups).m Explicit formulas for ordinary and bigraded Betti numbers for skeletons ofÌýcompact nonsingular toric varieties will be presented.Based on arXiv:2401.14146.