Papers
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Preprint
We show that a general Du Val pointed curve of genus g satisfies the Brill-Noether Theorem for pointed curves. Furthermore, we prove that a Du Val
pencil is disjoint from all Brill-Noether divisors on the universal curve. This provides explicit examples of smooth pointed curves of arbitrary genus defined over Q
which are Brill-Noether general.
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Submitted
The locus of genus-two curves with n marked Weierstrass points has codimension n inside the moduli space of genus-two 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
of the moduli space of stable genus-two curves with one marked point. We generalize this result for all n: we show that the class of the closure of the
locus of genus-two curves with n marked Weierstrass points spans an extremal ray of the cone of effective tautological classes of codimension n, for n<=6.
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To appear in Mathematische Zeitschrift
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 non-hyperelliptic 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.
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Journal of Algebra, Volume 454, 15 May 2016, pp. 1-13
Inside the symmetric product of a very general curve, we consider the codimension-one 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.
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Mathematical Research Letters, Volume 23, Number 2 (2016), pp. 389-404.
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 Fulton-Pragacz 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. 9569-9593
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.
Brill-Noether Loci in Codimension Two
Compositio Mathematica, Volume 149, Issue 09, September 2013, pp. 1535-1568
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 Brill-Noether 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, Volume 10, Issue 1, 2013, pp. 343–392
Double Points of Plane Models in M_{6,1}
Journal of Pure and Applied Algebra, Volume 216, Issue 4, April 2012, pp. 766-774
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 Brill-Noether number 0 or -1 is introduced to complete the computation.
Geometric Cycles in Moduli Spaces of Curves
PhD Thesis, Humboldt University in Berlin, 2012
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