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math.AG2025
Modular differential equations of minimal orders of the elliptic genus of Calabi--Yau varieties
Dmitrii Adler, Valery Gritsenko
We study modular differential equations (MDEs) of high orders for weak Jacobi forms and find necessary conditions for weak Jacobi forms to satisfy MDEs of order 3 with respect to t…
math.AG2010
Moduli spaces of polarised symplectic O'Grady varieties and Borcherds products
V. Gritsenko, K. Hulek, G. K. Sankaran
We study moduli spaces of O'Grady's ten-dimensional irreducible symplectic manifolds. These moduli spaces are covers of modular varieties of dimension 21, namely quotients of hermi…