Spring 2017 Boston CollegeNortheastern Algebraic Geometry Conference When: March 18, 2017, 10am5pm Where: West Village G 104, Northeastern University Speakers:
Schedule:
Abstracts Dan Abramovich  Resolution in toroidal orbifolds Igor Dolgachev  Decomposition and inertia subgroups of a group of birational automorphisms of an algebraic surface Abstract: I
will discuss a problem of whether an automorphism of an algebraic
surface of positive entropy can fix a smooth rational curve on the
surface pointwisely. This problem was raised by A. Coble
almost a hundred years ago and the first such example has been found
only recently by John Lesieutre. I will discuss an example of a group of
automorphisms of a rational or a K3 surface that is isomorphic to a
nonelementary discrete group of isometries of a hyperbolic space that
leaves a smooth rational curve invariant and hence admits a nontrivial
homomorphism to the group of Moebius transformations. The problem of
injectivity of this map is related to the problem of freeness of some
rotation group associated with a regular tetrahedron.
Montserrat Teixidor i Bigas  Line bundles on chains of elliptic curves and applications Abstract: Consider a degeneration of a curve of genus g to a chain of g elliptic curves. The linear series on the curves can be described in simple combinatorial terms that are suitable for computations. We used this approach for instance to calculate the genus of the BrillNoether locus and the method could potentially allow to compute the Eiuler Poincare characteristic of BrillNoether loci in general.This point of view can also help in dealing with other problems such as the maximal rank conjecture. Moreover, the combinatorial description can be easily compared with a tropical approach to BrillNoether for chains of loops. Xiaolei Zhao  Canonical points on K3 surfaces and hyperKähler varieties Abstract: The
Chow groups of algebraic cycles on algebraic
varieties have many mysterious properties. For K3 surfaces, on the one
hand, the Chow group of 0cycles is known to be huge. On the other hand,
the 0cycles arising from intersections of divisors and the second
Chern class of the tangent bundle all lie in
a one dimensional subgroup. A conjecture of Beauville and Voisin gives a
generalization of this property to hyperKähler varieties. In my talk, I
will recall these beautiful stories, and explain a conjectural
connection between the K3 surface case and the
hyperKähler case. Several examples will be discussed. This is based on
a joint work with Junliang Shen and Qizheng Yin.
