6,821 research outputs found
Positivity Of Equivariant Gromov–Witten Invariants
We show that the equivariant Gromov–Witten invariants of a projective homogeneous space G/P exhibit Graham-positivity: when expressed as polynomials in the positive roots, they have nonnegative coefficients
Equivariant Quantum Schubert Polynomials
We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the equivariant quantum cohomology ring, as well as Graham-positivity of the structure constants in equivariant quantum Schubert calculus. (C) 2013 Elsevier Inc. All rights reserved
Enumeration of rational plane curves tangent to a smooth cubic
We use twisted stable maps to compute the number of rational degree d plane
curves having prescribed contacts to a smooth plane cubic.Comment: 27 pages, v2: typos corrected and references adde
Pointed Trees Of Projective Spaces
We introduce a smooth projective variety T(d,n) which compactifies the space of configurations of it distinct points oil affine d-space modulo translation and homothety. The points in the boundary correspond to n-pointed stable rooted trees of d-dimensional projective spaces, which for d = 1, are (n + 1)-pointed stable rational curves. In particular, T(1,n) is isomorphic to ($) over bar (0,n+1), the moduli space of such curves. The variety T(d,n) shares many properties with (M) over bar (0,n+1). For example, as we prove, the boundary is a smooth normal crossings divisor whose components are products of T(d,i) for i \u3c n and it has an inductive construction analogous to but differing from Keel\u27s for (0,n+1). This call be used to describe its Chow groups and Chow motive generalizing [Trans. Airier. Math. Soc. 330 (1992), 545-574]. It also allows us to compute its Poincare polynomials, giving all alternative to the description implicit in [Progr. Math., vol. 129, Birkhauser, 1995, pp. 401-417]. We give a presentation of the Chow rings of T(d,n), exhibit explicit dual bases for the dimension I and codimension 1 cycles. The variety T(d,n) is embedded in the Fulton-MacPherson spaces X[n] for any smooth variety X, and we use this connection in a number of ways. In particular we give a family of ample divisors on T(d,n) and an inductive presentation of the Chow motive of X[n]. This also gives an inductive presentation of the Chow groups of X[n] analogous to Keel\u27s presentation for (M) over bar (0,n+1), solving a problem posed by Fulton and MacPherson
K-classes of Brill-Noether loci and a determinantal formula
We prove a determinantal formula for the K-theory class of certain degeneracy
loci, and apply it to compute the Euler characteristic of the structure sheaf
of the Brill-Noether locus of linear series with special vanishing at marked
points. When the Brill-Noether number is zero, we recover the
Castelnuovo formula for the number of special linear series on a general curve;
when , we recover the formulas of Eisenbud-Harris, Pirola, and
Chan-L\'opez-Pflueger-Teixidor for the arithmetic genus of a Brill-Noether
curve of special divisors.
Our degeneracy locus formula also specializes to new determinantal
expressions for the double Grothendieck polynomials corresponding to
321-avoiding permutations, and gives double versions of the flagged skew
Grothendieck polynomials recently introduced by Matsumura. Our result extends
the formula of Billey-Jockusch-Stanley expressing Schubert polynomials for
321-avoiding permutations as generating functions for skew tableaux.Comment: 31 pages; v2: stronger Theorem C, and improved expositio
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