# $Td_p$ notation of Kotschick

In this paper, notation $$Td_p$$ is used without explicit definition (it is stated that it is a certain combination of Chern numbers). It is claimed that HRR theorem implies $$Td_p(M)=\sum_{q}(-1)^q h^{p, q}(M)$$ for any closed complex manifold $$M$$.

Am I correct assuming that $$Td_p$$ stands for the pairing of $$Td(M)Ch(\Omega^p)$$ with the fundamental class of $$M$$? Here $$\Omega$$ is the canonical bundle.

The HRR-Theorem asserts $$\int Td(M)ch(E)=\chi(M,E)=\sum_q(-1)^q\dim H^q(M,E)$$ for every vector bundle $$E$$. With $$E=\Omega^p$$ the sheaf of holomorphic $$p$$-forms you get $$\int Td(M)ch(\Omega^p)=\sum_q(-1)^q\dim H^q(M,\Omega^p)=\sum_q(-1)^q h^{p,q}.$$ So your guess is right.