2 citations · 3 across the 10 of their papers we have counts for
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The Last Picard Rank 1 Double--Mirror Calabi--Yau Pair?
Michał Kapustka, Marco Rampazzo, Prajwal Samal
We consider a certain pair of families of Picard rank 1 Calabi--Yau threefolds, that have appeared earlier in mathematical literature in unrelated contexts: the family $\mathcal{X}…
Categorical reconstruction of del Pezzo surfaces: Hochschild--Serre algebras and spinor modifications
Xun Lin, Marco Rampazzo, Shizhuo Zhang
We prove that, for every smooth complex del Pezzo surface of degree at most four, the enhanced right orthogonal to the structure sheaf determines the surface up to isomorphism. In…
Categorical resolutions and birational geometry of nodal Gushel-Mukai varieties
Kacper Grzelakowski, Marco Rampazzo, Shizhuo Zhang
We study ordinary Gushel--Mukai varieties with one node in dimensions three, four, and five, under some generality hypotheses. The blowup of the node is related by a relative Atiya…
Window categories for a simple -fold flop of Grassmannian type
Will Donovan, Wahei Hara, Michał Kapustka +1
The local simple -fold flop of Grassmannian type is a birational transformation between total spaces of vector bundles on the Grassmannians and $\mathrm{Gr}(…
Derived equivalence for the simple flop of type
Marco Rampazzo, Ying Xie
We prove that every simple flop of type , i.e., resolved by blowups with exceptional divisor isomorphic to a generalized Grassmann bundle with fiber , induces a der…
Fano fibrations and DK conjecture for relative Grassmann flips
Marco Rampazzo
Given a vector bundle on a smooth projective variety , the flag bundle admits two projective bundle structures over the Grassmann bun…
Fullness of the Kuznetsov-Polishchuk exceptional collection for the spinor tenfold
Riccardo Moschetti, Marco Rampazzo
Kuznetsov and Polishchuk provided a general algorithm to construct exceptional collections of maximal length for homogeneous varieties of type A,B,C,D. We consider the case of the…
New counterexamples to the birational Torelli theorem for Calabi--Yau manifolds
Marco Rampazzo
We produce counterexamples to the birational Torelli theorem for Calabi-Yau manifolds in arbitrarily high dimension: this is done by exhibiting a series of non birational pairs of…
The generalized roof F(1,2,n): Hodge structures and derived categories
Enrico Fatighenti, Michał Kapustka, Giovanni Mongardi +1
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two projective bundle structures. Given a…
Calabi-Yau fibrations, simple K-equivalence and mutations
Marco Rampazzo
A homogeneous roof is a rational homogeneous variety of Picard rank 2 and index equipped with two different -bundle structures. We consider bundles of homogene…
Mukai duality via roofs of projective bundles
Michał Kapustka, Marco Rampazzo
We investigate a construction providing pairs of Calabi-Yau varieties described as zero loci of pushforwards of a hyperplane section on a roof as described by Kanemitsu. We discuss…
Torelli problem for Calabi-Yau threefolds with GLSM description
Michał Kapustka, Marco Rampazzo
We construct a gauged linear sigma model with two non-birational Kälher phases which we prove to be derived equivalent, -equivalent, deformation equivalent and Hodge eq…