We obtain new classes of singular equivalences which are constructed from Gorenstein-projective modules.

We prove that the locus of Prym curves (C,η) of genus g≥5 for which the Prym-canonical system |ωC(η)| is base point free but the Prym-canonical map is not an embedding is irreducible and unirational of dimension 2g+1.

We study L^p inequalities that sharpen the triangle inequality for sums of N functions in L^p.

Let G={h_t|t∈ℝ} be a continuous flow on a connected n-manifold M. The flow G is said to be strongly reversible by an involution τ if h_{−t}=τh_tτ for all t∈ℝ, and it is said to be periodic if h_s= identity for some s∈ℝ^∗. A closed subset K of M is called a global section for G if every orbit G(x) intersects K in exactly one point. In this paper, we study how the two properties “strongly reversible” and “has a global section” are related. In particular, we show that if G is periodic and strongly reversible by a reflection, then G has a global section.

We define tautological relations for the moduli space of stable maps to a target variety. Using the double ramification cycle formula for target varieties of Janda–Pandharipande–Pixton–Zvonkine, we construct non-trivial tautological relations parallel to Pixton’s double ramification cycle relations for the moduli of curves. Examples and applications are discussed.