Papers

In preparation
The locus of curves of genus two with n marked Weiestrass points has codimension n inside the moduli space of genus two, npointed curves, for 1<=n<=6.
We produce an explicit formula for the classes of these loci. The formula is expressed using a generating function over stable graphs indexing the boundary strata of
moduli spaces of pointed stable curves.

Submitted, arXiv:1705.02992
We prove a determinantal formula for the Ktheory class of certain degeneracy
loci, and apply it to compute the Euler characteristic of the structure sheaf
of the BrillNoether locus of linear series with special vanishing at marked
points. When the BrillNoether number \rho is zero, we recover the
Castelnuovo formula for the number of g^r_d's on a general curve; when
\rho=1, we recover the formulas of EisenbudHarris, Pirola, and
ChanLópezPfluegerTeixidor for the arithmetic genus of a BrillNoether
curve of special divisors.
Our degeneracy locus formula also specializes to new determinantal
expressions for the double Grothendieck polynomials corresponding to
321avoiding permutations, and gives double versions of the flagged skew
Grothendieck polynomials recently introduced by Matsumura. Our result extends
the formula of BilleyJockuschStanley expressing Schubert polynomials for
321avoiding permutations as generating functions for skew tableaux.

Selecta Mathematica, 23:3 (2017), pp. 22432259
We show that a general curve in an explicit class of what we call Du Val pointed curves satisfies the BrillNoether Theorem for pointed curves.
Furthermore, we prove that a generic pencil of Du Val pointed curves is disjoint from all BrillNoether divisors on the universal curve.
This provides explicit examples of smooth pointed curves of arbitrary genus defined over Q which are BrillNoether general.
A similar result is proved for 2pointed curves as well using explicit curves on elliptic ruled surfaces.

Algebra & Number Theory, 10:9 (2016), pp. 1935–1948
The locus of genustwo curves with n marked Weierstrass points has codimension n inside the moduli space of genustwo curves with n marked points,
for n<=6. It is well known that the class of the closure of the divisor obtained for n=1 spans an extremal ray of the cone of effective divisor classes.
We generalize this result for all n: we show that the class of the closure of the locus of genustwo curves with n marked Weierstrass points spans
an extremal ray of the cone of effective classes of codimension n, for n<=6. A related construction produces extremal nef curve classes in moduli spaces of pointed elliptic curves.

Mathematische Zeitschrift, 284:3 (2016), pp. 683–714
Inside the moduli space of curves of genus three with one marked point, we consider the locus of hyperelliptic curves with a marked Weierstrass point, and
the locus of nonhyperelliptic curves with a marked hyperflex. These loci have codimension two. We compute the classes of their closures in the moduli space
of stable curves of genus three with one marked point. Similarly, we compute the class of the closure of the locus of curves of genus four with an even
theta characteristic vanishing with order three at a certain point. These loci naturally arise in the study of minimal strata of Abelian differentials.

Journal of Algebra, 454 (2016), pp. 113
Inside the symmetric product of a very general curve, we consider the codimensionone subvarieties of symmetric tuples of points imposing exceptional
secant conditions on linear series on the curve of fixed degree and dimension. We compute the classes of such divisors, and thus obtain improved bounds for
the slope of the cone of effective divisor classes on symmetric products of a very general curve.
By letting the moduli of the curve vary, we study more generally the classes of the related divisors inside the moduli space of stable pointed curves.

Mathematical Research Letters, 23:2 (2016), pp. 389404.
The classical Castelnuovo numbers count linear series of minimal degree and fixed dimension on a general curve, in the case when this number is finite. For
pencils, that is, linear series of dimension one, the Castelnuovo specialize to the better known Catalan numbers. Using the FultonPragacz determinantal
formula for flag bundles and combinatorial manipulations, we obtain a compact formula for the number of linear series on a general curve having prescribed
ramification at an arbitrary point, in the case when the expected number of such linear series is finite. The formula is then used to solve some
enumerative problems on moduli spaces of curves.
Double Total Ramifications for Curves of Genus 2
International Mathematics Research Notices, 19 (2015), pp. 95699593
Inside the moduli space of curves of genus 2 with 2 marked points we consider the loci of curves admitting a map to P^1 of degree d totally ramified over the two marked points, for d>=2. Such loci have codimension two. We compute the class of their compactifications in the moduli space of stable curves. Several results will be deduced from this computation.
BrillNoether Loci in Codimension Two
Compositio Mathematica, 149:09 (2013), pp. 15351568
Let us consider the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k.
Since the BrillNoether number is equal to 2, such a locus has codimension two.
Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves.
Extended abstract for Oberwolfach talk, in Oberwolfach Reports, 10:1 (2013), pp. 343–392
Double Points of Plane Models in M_{6,1}
Journal of Pure and Applied Algebra, 216:4 (2012), pp. 766774
The aim of this paper is to compute the class of the closure of the effective divisor
in M_{6,1} given by pointed curves [C,p] with a sextic plane model mapping p to a double point.
Such a divisor generates an extremal ray in the pseudoeffective cone of M_{6,1} as shown by Jensen.
A general result on some families of linear series with adjusted BrillNoether number 0 or 1 is introduced to complete the computation.
Geometric Cycles in Moduli Spaces of Curves
PhD Thesis, Humboldt University in Berlin, 2012
