Spring 2015 BC-Northeastern Algebraic Geometry ConferenceAna-Maria Castravet, Dawei Chen, Maksym Fedorchuk, Brian Lehmann, Emanuele Macri, and Alina MarianOrganized by: April 25, 2015, 10am-5pmWhen: 315 Shillman Hall, Northeastern UniversityWhere: Please register so that we have a headcount for coffee breaks. Registration: Speakers: - Brian Lehmann (Boston College)
- Paolo Stellari (Università degli Studi di Milano)
- Yuri Tschinkel (New York University)
- Filippo Viviani (Università Roma Tre)
Titles and schedule (subject to minor changes):
Abstracts:Brian Lehmann:
Zariski decompositions for curve classesAbstract: The Zariski decomposition is an important tool for understanding the
sections of a divisor on a surface. We discuss a generalization to
curves on varieties of arbitrary dimension. We give a number of
examples and applications to birational geometry. Paolo Stellari: Stability Conditions on Abelian and some Calabi-Yau ThreefoldsAbstract: We prove that a Bogomolov-Gieseker type inequality holds for abelian threefolds and some smooth projective Calabi-Yau threefolds of quotient type. This was conjectured by Bayer, Macri' and Toda. From this one deduces that the corresponding spaces of Bridgeland stability conditions are not empty. This is joint work with A. Bayer and E. Macri'. Yuri Tschinkel: K3 surfaces and their punctual Hilbert schemesAbstract: I will talk about birational geometry of holomorphic
symplectic varieties arising as deformations of punctual Hilbert schemes
of K3 surfaces (joint with Brendan Hassett). Filippo Viviani: Fourier-Mukai and autoduality for compactified Jacobians Abstract: To every reduced (projective) curve X with planar singularities one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, which are birational (possibly non-isomorphic) singular Calabi-Yau projective varieties, each of which yields a modular compactification of a disjoint union of copies of the generalized Jacobian of X. We define a Poincar\'e sheaf on the product of any two (possibly equal) fine compactified Jacobians of X and show that the associated integral transform is an equivalence of their derived categories, hence it defines a Fourier-Mukai transform. This generalizes the classical result of S. Mukai for Jacobians of smooth curves and the more recent result of D. Arinkin for compactified Jacobians of integral curves with planar singularities, and it provides further evidence for the classical limit of the geometric Langlands conjecture (as formulated by Donagi and Pantev). As a corollary, we prove that there is a canonical isomorphism (called autoduality) between the generalized Jacobian of X and the connected component of the identity of the Picard scheme of any fine compactified Jacobian of X and that algebraic equivalence and numerical equivalence coincide on any fine compactified Jacobian. This is a joint work with M. Melo and A. Rapagnetta. |