We use tropical techniques to prove a case of the Gieseker-Petri Theorem. Specifically, we show that the general curve of arbitrary genus does not admit a Gieseker-Petri special pencil.

2012-05-17math.AG

A codimension 2 component of the Gieseker-Petri locus

We show that the Brill-Noether locus M^3_{18,16} is an irreducible component of the Gieseker-Petri locus in genus 18 having codimension 2 in the moduli space of curves. This result disproves a conjecture predicting that the Gieseker-Petri locus is always divisorial.

2021-01-17math.AG

The Gieseker-Petri divisor in M_g for genus g<=13

The Gieseker-Petri locus GP_g is defined as the locus inside M_g consisting of curves which violate the Gieseker-Petri Theorem. It is known that GP_g has always some divisorial components and it has been conjectured that it is of pure codimension 1 inside M_g. We prove that this holds true for genus up to 13.

2010-12-14math.AG

Extremal effective divisors of Brill-Noether and Gieseker-Petri type in $\overline{\mathcal M}_{1,n}$

We show that certain divisors of Brill-Noether and Gieseker-Petri type span extremal rays of the effective cone in the moduli space of stable genus one curves with $n$ ordered marked points. In particular, they are different from the infinitely many extremal rays found in \cite{ChenCoskun}.

2014-07-18math.AG

Tropical Independence I: Shapes of Divisors and a Proof of the Gieseker-Petri Theorem

We develop a framework to apply tropical and nonarchimedean analytic techniques to multiplication maps on linear series and study degenerations of these multiplications maps when the special fiber is not of compact type. As an application, we give a tropical criterion for a curve over a valued field to be Gieseker-Petri general.

2014-11-02math.AG

The Gieseker-Petri theorem and imposed ramification

We prove a smoothness result for spaces of linear series with prescribed ramification on twice-marked elliptic curves. In characteristic 0, we then apply the Eisenbud-Harris theory of limit linear series to deduce a new proof of the Gieseker-Petri theorem, along with a generalization to spaces of linear series with prescribed ramification at up to two points. Our main calculation involves the intersection of two Schubert cycles in a Grassmannian associated to almost-transverse flags.

2020-10-28math.AG

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Gaussian maps, Gieseker-Petri loci and large theta-characteristics

We analyze the stratification of the moduli space S_g of spin curves of genus g given by the dimension of the theta-characteristic. Using the relation between gaussian maps and the strata S_g^r, we construct "regular" components of S_g^r having expected codimension r(r+1)/2 inside S_g. We also relate moduli spaces of pointed curves with a moving spin structure to the classical Gieseker-Petri loci in M_g. We show that the locus of curves for which the Gieseker-Petri theorem fails for a pencil is always a divisor on M_g. Finally, we give a sufficient criterion for the injectivity of Gaussian map…

2004-04-05math.AG

Rational maps between moduli spaces of curves and Gieseker-Petri divisors

We perform an intersection theoretic study of the rational map between two different moduli spaces of stable curves which associates to a curve its corresponding Brill-Noether locus (in the case this locus has virtual dimension 1). We then use these results to describe the cone of moving divisors on M_g. Several other applications to moduli spaces of Prym varieties are presented. In a different direction, we prove that the locus in M_g of curves failing to satisfy the Gieseker-Petri theorem is supported in codimension 1 for every possible type of linear series.

2009-05-09math.AG

A Gieseker type degeneration of moduli stacks of vector bundles on curves

Given a generically smooth stable curve over a discrete valuation ring such that its special fibre is irreducible with one double point, we construct a moduli stack over that descrete valuation ring which is a model for the moduli stack of vector bundles over the generic fibre of the curve. The model has the following nice properties: 1. It is regular. 2. Its special fibre is a normal crossing divisor. 3. The normalization of its special fibre is a locally trivial KGl-bundle over the moduli stack of vector bundles over the normalization of the special fibre of the curve. Here KGl is a canonica…

2002-01-21math.AG

A Petri Theorem for Rank 2 Bundles with Canonical Determinant

This paper establishes the correctness of a conjecture of Bertram-Feinberg and Mukai for a special class of globally generated rank-two bundles with canonical determinant over a generic Riemann surface of genus at least four.

2002-07-05math.AG

一般k-边曲线上特殊除子方案的光滑性结果

Smoothness results for the schemes of special divisors on general k-gonal curves

本文研究一般k-边曲线C上的特殊除子方案W^r_d(C)的光滑性，通过Brill-Noether退化方案的细化，证明其在特定开子集上光滑，并探讨invertible sheaves的Petri映射性质。

2026-03-24math.AG