arXiv subjects

Matthew M. Williams

Publications and source records attributed to Matthew M. Williams.

2 recordsLinked to original sources

arXiv2025

Quadratic Pseudostable Hodge Integrals and Mumford's Relations

This paper studies the relationship between quadratic Hodge classes on moduli spaces of pseudostable and stable curves given by the contraction morphism $\mathcal{T}.$ While Mumford relations do not hold in the pseudostable case, we show that one can express the (pullback via $\mathcal{T}$ of the) Chern classes of $\mathbb{E}\oplus \mathbb{E}^\vee$ solely in terms of descendants and strata classes. We organize the combinatorial structure of the pullback of products of two pseudostable $λ$ classes and obtain an explicit comparison of arbitrary pseudostable and stable quadratic Hodge integrals.

math.AG↗

arXiv2020

Mirror Symmetry for Nonabelian Landau-Ginzburg Models

We consider Landau-Ginzburg models stemming from groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group $G^\star$, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors for Fermat type polynomials., we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors for Fermat type polynomials.

math.AG↗