Representations of vertex operator algebras define sheaves of coinvariants and conformal
blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity …

We show that coinvariants of modules over vertex operator algebras give rise to
quasicoherent sheaves on moduli of stable pointed curves. These generalize Verlinde …

We introduce and study the problem of finding necessary and sufficient conditions under
which a conformal blocks divisor on M¯ 0, n M _ 0, n is nonzero, solving the problem …

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Basepoint free cycles on the moduli space of stable-pointed rational curves, defined using
Gromov–Witten invariants of smooth projective homogeneous spaces are introduced and …

We describe a relation between the invariants of n ordered points in projective d-space and
of points contained in a union of two linear subspaces. This yields an attaching map for GIT …

We consider a conjecture that identifies two types of base point free divisors on M¯ 0, n. The
first arises from Gromov-Witten theory of a Grassmannian. The second comes from first …

We develop new characteristic-independent combinatorial criteria for semiampleness of
divisors on M0, n. As an application, we associate to a cyclic rational quadratic form …

We complete Mori's program with symmetric divisors for the moduli space of stable seven-
pointed rational curves. We describe all birational models in terms of explicit blow-ups and …

For any simple Lie algebra, a positive integer, and n-tuple of compatible weights, the
conformal blocks bundle is a globally generated vector bundle on the moduli space of …