6 papers
Real Lagrangians in Calabi-Yau Threefolds
Hülya Argüz, Thomas Prince
We compute the mod cohomology groups of real Lagrangians in Calabi-Yau threefolds using well-behaved torus fibrations constructed by Gross. To do this we study a long exact seq…
From Cracked Polytopes to Fano Threefolds
Thomas Prince
We construct Fano threefolds with very ample anti-canonical bundle and Picard rank greater than one from cracked polytopes - polytopes whose intersection with a complete fan forms…
Polygons of Finite Mutation Type
Thomas Prince
We classify Fano polygons with finite mutation class. This classification exploits a correspondence between Fano polygons and cluster algebras, refining the notion of singularity c…
Cracked Polytopes and Fano Toric Complete Intersections
Thomas Prince
We introduce the notion of cracked polytope, and - making use of joint work with Coates and Kasprzyk - construct the associated toric variety as a subvariety of a non-singular…
Del Pezzo surfaces with a single 1/k(1,1) singularity
Daniel Cavey, Thomas Prince
Inspired by the recent progress by Coates-Corti-Kasprzyk et al. on Mirror Symmetry for del Pezzo surfaces, we show that for any positive integer k the deformation families of del P…
Laurent Inversion
Tom Coates, Alexander Kasprzyk, Thomas Prince
There are well-understood methods, going back to Givental and Hori--Vafa, that to a Fano toric complete intersection X associate a Laurent polynomial f that corresponds to X under…