Eric M. Rains

collaborators

3 papers

math.AG2024

Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets

Alexander Polishchuk, Eric Rains

We prove that for every relatively prime pair of integers $(d, r)$ with $r > 0$ , there exists an exceptional pair $(O, V)$ on any del Pezzo surface of degree 4, such that $V…

math.AG2024

Algebra of global sections of $ψ$ -bundles on $M ˉ_{0, n}$

Alexander Polishchuk, Eric Rains

We consider the $Z^{n}$ -graded algebra of global sections of line bundles generated by the standard line bundles $L_{1}, \dots, L_{n}$ on $M ˉ_{0, n}$ . We find a simple prese…

math.CO2016

A Nekrasov-Okounkov formula for Macdonald polynomials

Eric M. Rains, S. Ole Warnaar

We prove a Macdonald polynomial analogue of the celebrated Nekrasov-Okounkov hook-length formula from the theory of random partitions. As an application we obtain a proof of one of…

Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets

Algebra of global sections of ψ-bundles on Mˉ0,n​

A Nekrasov-Okounkov formula for Macdonald polynomials

Algebra of global sections of $ψ$ -bundles on $M ˉ_{0, n}$