University of Utah

Department of Mathematics


Algebraic Geometry Seminar


For information on the upcoming Western Algebraic Geometry seminar, April 24th and 25th, click here.


    Spring 1999 Lectures

Regular Meetings:  3:30-4:30pm Wednesdays, JFB102.
Occasionally, we may have additional lectures;  please see the schedule.
20 January Jian Kong  (University of Utah)
Seshadri constants of Abelian varieties
27 January Aaron Bertram  (University of Utah) 
Counting rational curves with a  torus of a different color
3 February János Kollár  (University of Utah)
Rationally connected varieties over local fields
10 February No talk
17 February Christopher Hacon (University of Utah)
Remarks on Seshadri constants of vector bundles 
24 February No talk
3 March Sorin Popescu (Columbia and MSRI)
Syzygies of subcanonical subschemes.  Abstract:  I will describe joint work with D. Eisenbud and Ch. Walter on 
resolutions by vector bundles. The idea is that coherent sheaves on projective  space which are symmetric in a suitable sense have symmetric vector bundle resolutions. This generalizes results on surfaces with even sets of nodes, theta characteristics of plane curves, self-linked space curves, and recent results of Catanese, Kleiman-Lipman-Ulrich, Walter and others. 
     I will also describe a structure result for Gorenstein subcanonical projective subschemes of codimension 3, and construct examples of smooth codimension 3 subcanonical varieties which are not Pfaffian (a projective subscheme of codimension 3 is Pfaffian if it is the degeneracy locus of a skew-symmetric morphism f : E^* --> E(t) with E a vector bundle of odd rank.)
Friday 3:30 pm in JWB 308
5 March Yuri Tschinkel  (University of Illinois at Chicago)
Points on rational varieties.   Abstract:  We study the distribution of rational points of bounded height 
on varieties closely related to linear algrebraic groups.
10 March Mohan Ramachandran (SUNY Buffalo)
On Complex hyperbolic manifolds and their structure at infinity
17 March No talk (spring break)
24 March Wiesia Niziol (Utah)
Semi-stable conjecture for vertical log-smooth fibrations
Monday 3:30 pm in JFB 102
29 March Adrian Vasiu (UC Berkeley)
Shimura varieties and the Mumford-Tate conjecture   Abstract
31 March Boris Dubrovin (SISSA and MSRI)
Elliptic Gromov-Witten invariants and tau-functions
7 April Ravi Vakil (M.I.T.)
Twelve points on the projective line.  Abstract:  There are many ways to geometrically define a (PGL(2)-invariant) divisor in the variety of "12 points in P^1", Sym^{12}(P^1), isomorphic to P^{12}.  For example:  the 12 nodal cubics in a pencil of plane cubics; the branch points of a degree 4 map of a genus 3 hyperelliptic curve to P^1; the branch points of a genus 3 curve mapped to P^1 by the canonical sheaf; the branch points of a genus 4 curve mapped to P^1 by a theta-characteristic.  We'll see that these divisors (and others) are all the same, by showing that the corresponding moduli spaces are covers of others.  The links involve various beautiful classical constructions.
14 April Bill Lang (Brigham Young University)
  Pathologies of algebraic surfaces in characteristic p
21 April Alexander Buium (University of Illinois at Urbana/Champaign) 
Arithmetic jet spaces
24, 25 April WAGS
28 April Rick Miranda (Colorado State University)
Linear Systems of Plane Curves with Prescribed Multiplicities: New Approaches to the Harbourne-Hirschowitz Conjecture

Speakers and the titles from past terms:   Fall 1997, Winter 1998 , Spring 1998. Fall 1998.


We maintain an emailing list for special announcements,  extra talks etc.  To be added to or deleted from this list, or with questions or comments about the seminar, email Holger Kley at

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