Introduces categorical absorption of singularities for projective varieties with isolated ordinary double points and shows the smooth part extends over smoothings.
Categorical cones and quadratic homological projective duality
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction provides well-behaved categorical resolutions of singular quadrics, which we use to obtain an explicit quadratic version of the main theorem of homological projective duality. As applications, we prove the duality conjecture for Gushel-Mukai varieties, and produce interesting examples of conifold transitions between noncommutative and honest Calabi-Yau threefolds.
fields
math.AG 2years
2022 2verdicts
UNVERDICTED 2representative citing papers
Proves generalized Hodge, Mumford-Tate and Tate conjectures for GM varieties, computes most Chow groups, and establishes motive isomorphisms for partners and duals.
citing papers explorer
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Categorical absorptions of singularities and degenerations
Introduces categorical absorption of singularities for projective varieties with isolated ordinary double points and shows the smooth part extends over smoothings.
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Algebraic cycles on Gushel-Mukai varieties
Proves generalized Hodge, Mumford-Tate and Tate conjectures for GM varieties, computes most Chow groups, and establishes motive isomorphisms for partners and duals.