108 citations · 436 across the 24 of their papers we have counts for
18 papers · 1 filter
Effective Categorical Enumerative Invariants
Andrei Caldararu, Junwu Tu
We introduce enumerative invariants , associated to a cyclic algebra and a splitting of its non-commutative Hodge filtration. These invari…
The cup product in orbifold Hochschild cohomology
Andrei Caldararu, Shengyuan Huang
We study the multiplicative structure of orbifold Hochschild cohomology in an attempt to generalize the results of Kontsevich and Calaque-Van den Bergh relating the Hochschild and…
Categorical primitive forms and Gromov-Witten invariants of singularities
Andrei Caldararu, Si Li, Junwu Tu
We introduce a categorical analogue of Saito's notion of primitive forms. Let denote the potential . For the category of matrix factorizations of…
Computing a categorical Gromov-Witten invariant
Andrei Caldararu, Junwu Tu
We compute the B-model Gromov-Witten invariant of an elliptic curve E directly from the derived category D(E). More precisely, we carry out the computation of the catego…
Intersections of two Grassmannians in
Lev A. Borisov, Andrei Caldararu, Alexander Perry
We study the intersection of two copies of embedded in , and the intersection of the two projectively dual Grassmannians in the dual projective spa…
Formality of derived intersections and the orbifold HKR isomorphism
Dima Arinkin, Andrei Caldararu, Marton Hablicsek
We study when the derived intersection of two smooth subvarieties of a smooth variety is formal. As a consequence we obtain a derived base change theorem for non-transversal inters…
Derived intersections and the Hodge theorem
Dima Arinkin, Andrei Caldararu, Marton Hablicsek
The algebraic Hodge theorem was proved in a beautiful 1987 paper by Deligne and Illusie, using positive characteristic methods. We argue that the central algebraic object of their…
On the Lie algebroid of a derived self-intersection
Damien Calaque, Andrei Caldararu, Junwu Tu
Let be a closed embedding of smooth algebraic varieties. Denote by the normal bundle of in . We describe the construction of two Lie-type structur…
When is the self-intersection of a subvariety a fibration?
Dima Arinkin, Andrei Caldararu
We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequenc…
The Mukai pairing, I: a categorical approach
Andrei Caldararu, Simon Willerton
We study the Hochschild homology of smooth spaces, emphasizing the importance of a pairing which generalizes Mukai's pairing on the cohomology of K3 surfaces. We show that integral…
The Pfaffian-Grassmannian derived equivalence
Lev Borisov, Andrei Caldararu
We argue that there exists a derived equivalence between Calabi-Yau threefolds obtained by taking dual hyperplane sections (of the appropriate codimension) of the Grassmannian G(2,…
Fiberwise stable bundles on elliptic threefolds with relative Picard number one
Andrei Caldararu
We show that fiberwise stable vector bundles are preserved by relative Fourier-Mukai transforms between elliptic threefolds with relative Picard number one. Using these bundles we…
Non-birational Calabi-Yau threefolds that are derived equivalent
Andrei Caldararu
We argue that the existence of genus one fibrations with multisections of high degree on certain Calabi-Yau threefolds implies the existence of pairs of such varieties that are not…
Derived categories of sheaves: a skimming
Andrei Caldararu
These lecture notes were prepared for the workshop ``Algebraic Geometry: Presentations by Young Researchers'' in Snowbird, Utah, July 2004, and for the autumn school in Lukecin, Po…
The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism
Andrei Caldararu
We continue the study of the Hochschild structure of a smooth space that we began in our previous paper, examining implications of the Hochschild-Kostant-Rosenberg theorem. The mai…
The Mukai pairing, I: the Hochschild structure
Andrei Caldararu
We study the Hochschild structure of a smooth space or orbifold, emphasizing the importance of a pairing defined on Hochschild homology which generalizes a similar pairing introduc…
Non-Fine Moduli Spaces of Sheaves on K3 Surfaces
Andrei Caldararu
In general, if M is a moduli space of stable sheaves on X, there is a unique alpha in the Brauer group of M such that a pi_M^* alpha^{-1}-twisted universal sheaf exists on X times…
Derived Categories of Twisted Sheaves on Elliptic Threefolds
Andrei Caldararu
We construct an equivalence between the derived category of sheaves on an elliptic threefold without a section and a derived category of twisted sheaves (modules over an Azumaya al…