Spring 2017

Spring 2017 Boston College-Northeastern Algebraic Geometry Conference

When:
March 18, 2017, 10am-5pm
Where:
West Village G 104, Northeastern University


Speakers:

Registration: simply fill out a short registration form (needed for a headcount for coffee breaks and lunch)

Schedule:

 10-11am
  
 11-11:30am
 
 11:30am-12:30pm


 12:30-2pm


 2-3pm

 3-3:30pm 
 
 3:30-4:30pm
 Dan Abramovich --- Resolution in toroidal orbifolds 

 Coffee break
 
 Montserrat Teixidor i Bigas --- Line bundles on chains of elliptic curves and applications

Lunch break

Xiaolei Zhao --- Canonical points on K3 surfaces and hyper-Kähler varieties


 Coffee break

 
Igor Dolgachev --- Decomposition and inertia subgroups of a group of birational automorphisms of an algebraic surface


Abstracts


Dan Abramovich --- Resolution in toroidal orbifolds

Abstract: A beginner can easily resolve toric singularities. While enormous progress was made on simplifying characteristic-0 resolution of singularities in general, wouldn't it be nice to have a straightforward way to transform any singularity to a toric singularity?
    In joint work with Michael Temkin (Jerusalem) and Jarosław Włodarczyk (Purdue) we principalize an ideal, making it monomial on a variety which has only toroidal singularities, leading to such transformation, albeit using the language of stacks.
    I'll show how this works in explicit examples.


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  non-elementary discrete group of isometries of a hyperbolic space that leaves a smooth rational curve invariant and hence admits a non-trivial 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 Brill-Noether locus and the method could  potentially allow to  compute the Eiuler Poincare characteristic of Brill-Noether 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 Brill-Noether for chains of loops.


Xiaolei Zhao --- Canonical points on K3 surfaces and hyper-Kähler 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 0-cycles is known to be huge. On the other hand, the 0-cycles 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 hyper-Kähler varieties. In my talk, I will recall these beautiful stories, and explain a conjectural connection between the K3 surface case and the hyper-Kähler case. Several examples will be discussed. This is based on a joint work with Junliang Shen and Qizheng Yin.


Organized by: Ana-Maria Castravet, Dawei Chen, Qile Chen, Maksym Fedorchuk, Brian Lehmann, Emanuele Macri, and Alina Marian

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