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ESSENTIAL DIMENSION OF MODULI OF CURVES AND OTHER ALGEBRAIC STACKS (WITH AN APPENDIX BY NAJMUDDIN FAKHRUDDIN)
ESSENTIAL DIMENSION OTHER ALGEBRAIC STACKS
2015/9/29
In this paper we consider questions of the following type.
Let k be a base eld and K=k be a eld extension. Given a geometric
object X over a eld K (e.g. a smooth curve of genus g) what is the
le...
In the study of the geometry of curves on surfaces, the following
question often arises: given a one-parameter family of divisors over a pointed
curve, what does the central ber look like after sta...
The Plateau problem for polygonal boundary curves in Minkowski 3-space
maximal immersions with singularities integrable systems
2011/2/21
We apply Garnier’s method to solve the Plateau problem for maximal surfaces in Minkowski 3-space. Our study relies on the improved version we gave in [4] of Garnier’s resolution [12] of the Plateau pr...
We prove that the Chow quotient parametrizing configurations of n points in Pd which generically lie on a rational normal curve is isomorphic to M0,n, generalizing the well-known d = 1 result of Kapra...
This is the first in a projected series of three papers in which we construct the second flip in the log minimal model program for Mg. We introduce the notion of a weakly proper algebraic stack.
Determinantal representation and subschemes of general plane curves
Determinantal representation subschemes of general plane curves
2011/2/21
Let M = (mij ) be an n × n square matrix of integers. For our purposes, we can assume without loss of generality that M is homogeneous and that the entries are non-increasing going leftward and downwa...
Characteristic numbers of rational nodal curves in $\mathbb{P}^3$
Characteristic numbers of rational nodal $\mathbb{P}^3$
2011/1/19
In this paper we compute the number of rational curves with one node passing through a given number of points, lines and tangent to a given number of planes in P3.
Noncommutative Tate curves
ate curves UHF-algebras
2011/1/17
It is proved, that the homology group of the Tate curve is the Pontryagin dual to the K-theory of the UHF-algebras.
We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classi cation of modular compacti cations of Mg;n, and t...
On the rational Picard group of the moduli space of curves
rational Picard group moduli space of curves
2011/2/25
We speculate about an algebro-geometric proof of Harer’s theorem on the rational Picard group of the moduli space of smooth complex curves. In particular, we refine the approach of Diaz and Edidin in-...
Two families of maximal curves which are not Galois subcovers of the Hermitian curve
maximal curves generalized GK curves Galois coverings
2011/1/20
We show that the generalized Giulietti-Korchm´aros curve and the maximal curve with equation x q2 − x = y (qn+1)/(q+1) defined over F q2n, for n 3 odd and q 3, are not Galois subcovers...
Giulietti and Korchm´aros presented new curves with the maximal number of points over a field of size q6. Garcia, G¨uneri, and Stichtenoth extended the construction to curves that are maximal ov...
For a domain D ⊂ Cn we construct a continuous fo-liation of D into one real dimensional curves such that any func-tion f ∈ C1(D) which can be extended holomorphically into some
neighborhood of ...
Counting lattice points in compactified moduli spaces of curves
Counting lattice points compactified moduli spaces of curves
2011/3/1
We define and count lattice points in the moduli spaceMg,n of stable genus g curves with n labeled points.
We show that projective K3 surfaces with odd Picard rank contain infinitely many rational curves. Our proof extends the Bogomolov-Hassett-Tschinkel approach, i.e., uses moduli spaces of stable maps an...