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26
Variation of Geometric Invariant Theory quotients and derived categories
, 2014
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Derived categories of Burniat surfaces and exceptional
, 2013
"... Abstract. We construct an exceptional collection Υ of maximal possible length 6 on any of the Burniat surfaces with K2X = 6, a 4dimensional family of surfaces of general type with pg = q = 0. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generate ..."
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Abstract. We construct an exceptional collection Υ of maximal possible length 6 on any of the Burniat surfaces with K2X = 6, a 4dimensional family of surfaces of general type with pg = q = 0. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal com
Homological Projective Duality via Variation of Geometric Invariant Theory Quotients
, 2014
"... We provide a geometric approach to constructing Lefschetz collections and LandauGinzburg Homological Projective Duals from a variation of Geometric Invariant Theory quotients. Additionally, we provide a description of the derived category of a degree d hypersurface fibration which recovers Kuznets ..."
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Cited by 9 (3 self)
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We provide a geometric approach to constructing Lefschetz collections and LandauGinzburg Homological Projective Duals from a variation of Geometric Invariant Theory quotients. Additionally, we provide a description of the derived category of a degree d hypersurface fibration which recovers Kuznetsov’s result for quadric fibrations. Combining these two approaches yields homological projective duals for Veronese embeddings. We also extend the Homological Projective Duality framework to the relative setting for all of our results.
Height of exceptional collections and Hochschild cohomology of quasiphantom categories, preprint arXiv:1211.4693
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Exceptional collections on 2adically uniformised fake projective planes, preprint arXiv:1310.3020
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AbelJacobi maps for hypersurfaces and non commutative CalabiYau’s
 Comm. Cont. Math
"... Abstract. It is well known that the Fano scheme of lines on a cubic 4fold is a symplectic variety. We generalize this fact by constructing a closed (2n − 4)form on the Fano scheme of lines on a (2n − 2)dimensional hypersurface Yn of degree n. We provide several definitions of this form — via the ..."
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Cited by 3 (0 self)
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Abstract. It is well known that the Fano scheme of lines on a cubic 4fold is a symplectic variety. We generalize this fact by constructing a closed (2n − 4)form on the Fano scheme of lines on a (2n − 2)dimensional hypersurface Yn of degree n. We provide several definitions of this form — via the Abel–Jacobi map, via Hochschild homology, and via the linkage class — and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Yn we show that the Fano scheme is birational to a certain moduli space of sheaves of a (2n−4)dimensional Calabi–Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual CalabiYau becomes non commutative.