Modules over conformal vertex algebras give rise to sheaves of coinvariants and blocks on moduli stable pointed curves. Here we prove the factorization conjecture for these sheaves. Our results apply in arbitrary genus a large class algebras. As an application, defined by finitely generated admissible modules satisfying natural hypotheses are shown be vector bundles. Factorization is essential recursive formulation invariants, like ranks Chern classes, produce new constructions rational...

Abstract We compute the Euler characteristic of structure sheaf Brill–Noether locus linear series with special vanishing at up to two marked points. When number $\rho $ is zero, we recover Castelnuovo formula for on a general curve; when =1$, formulas Eisenbud-Harris, Pirola, and Chan–Martín–Pflueger–Teixidor arithmetic genus curve divisors. These computations are obtained as applications new determinantal $K$-theory class certain degeneracy loci. Our also specializes expressions double...

Abstract Let us consider the locus in moduli space of curves genus $2k$ defined by with a pencil degree $k$ . Since Brill–Noether number is equal to $- 2$ , such has codimension two. Using method test surfaces, we compute class its closure stable curves.

Abstract. 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, one, specialize to better known Catalan numbers. Using Fulton-Pragacz determinantal formula for flag bundles combinatorial manipulations, we obtain compact curve having prescribed ramification at an arbitrary point, expected such then used solve some enumerative problems moduli spaces curves.

The locus of genus-two curves with n marked Weierstrass points has codimension inside the moduli space points, for n<=6. It is well known that class closure divisor obtained n=1 spans an extremal ray cone effective classes. We generalize this result all n: we show classes n, A related construction produces nef curve in spaces pointed elliptic curves.

We compute the Euler characteristic of structure sheaf Brill-Noether locus linear series with special vanishing at up to two marked points. When number $ρ$ is zero, we recover Castelnuovo formula for on a general curve; when $ρ=1$, formulas Eisenbud-Harris, Pirola, and Chan-Martín-Pflueger-Teixidor arithmetic genus curve divisors. These computations are obtained as applications new determinantal K-theory class certain degeneracy loci. Our also specializes expressions double Grothendieck...

Journal Article Double Total Ramifications for Curves of Genus 2 Get access Nicola Tarasca Department Mathematics, University Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA Correspondence to be sent to: tarasca@math.utah.edu Search other works by this author on: Oxford Academic Google Scholar International Mathematics Research Notices, Volume 2015, Issue 19, Pages 9569–9593, https://doi.org/10.1093/imrn/rnu228 Published: 02 December 2014 history Received: 12 February Revision received: 26...

We show that coinvariants of modules over vertex operator algebras give rise to quasi-coherent sheaves on moduli stable pointed curves. These generalize Verlinde bundles or vector conformal blocks defined using affine Lie studied first by Tsuchiya-Kanie, Tsuchiya-Ueno-Yamada, and extend work a number researchers. The carry twisted logarithmic D-module structure, hence support projectively flat connection. identify the Atiyah algebra acting them, generalizing Tsuchimoto for algebras.

We study the codimension <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> locus of curves genus alttext="2"> <mml:mn>2</mml:mn> encoding="application/x-tex">2</mml:annotation> with distinct marked Weierstrass points inside moduli space </inline-formula>, </inline-formula>-pointed...

Representations of vertex operator algebras define sheaves coinvariants and conformal blocks on moduli stable pointed curves. Assuming certain finiteness semisimplicity conditions, we prove that such satisfy the factorization conjecture consequently are vector bundles. Factorization is essential to a recursive formulation invariants, like ranks Chern classes, produce new constructions rational field theories cohomological theories.

Inside the moduli space of curves genus three with one marked point, we consider locus hyperelliptic a Weierstrass and non-hyperelliptic hyperflex. These loci have codimension two. We compute classes their closures in stable point. Similarly, class closure four an even theta characteristic vanishing order at certain naturally arise study minimal strata Abelian differentials.

For a triple consisting of weakly negative definite plumbed 3-manifold, root lattice, and generalized $\mathrm{Spin}^c$-structure, we construct family invariants in the form Laurent series. Each series is an invariant up to orientation preserving homeomorphisms action Weyl group. We show that there are infinitely many such for irreducible lattices rank at least 2, with each depending on solution combinatorial puzzle defined lattice. Our recover certain related recently by...

Over the moduli space of pointed smooth algebraic curves, projectivized $k$-th Hodge bundle is $k$-canonical divisors. The incidence loci are defined by requiring divisors to have prescribed multiplicities at marked points. We compute classes closure in over curves with rational tails. expressed as a linear combination tautological indexed decorated stable graphs coefficients enumerating appropriate weightings. As consequence, we obtain an explicit expression for some relations rings

Motivic Chern and Hirzebruch classes are polynomials with K-theory homology as coefficients, which specialize to Chern–Schwartz–MacPherson classes, Cappell–Shaneson L-classes. We provide formulas compute the motivic of Grassmannian vexillary degeneracy loci. apply our results obtain χ y $\chi _y$ -genus classical one-pointed Brill–Noether varieties, therefore their topological Euler characteristic, holomorphic signature.

We construct pointed Prym–Brill–Noether varieties parametrizing line bundles assigned to an irreducible étale double covering of a curve with prescribed minimal vanishing at fixed point. realize them as degeneracy loci in type D and deduce their classes case expected dimension. Thus, we determine Prym–Petri map prove version the theorem implying that dimension holds general case. These results build on work Welters [Ann. Sci. Ëcole Norm. Sup. (4) 18 (1985), pp. 671–683] De Concini–Pragacz...

Representations of certain vertex algebras, here called CohFT-type, can be used to construct vector bundles coinvariants and conformal blocks on moduli spaces stable curves [DGT2]. We show that such define semisimple cohomological field theories. As an application, we give expression for their total Chern character in terms the fusion rules, following approach computation [MOPPZ] given by integrable modules over affine Lie algebras. It follows classes are tautological. Examples open problems...

Over the moduli space of pointed smooth algebraic curves, projectivized $k$-th Hodge bundle is $k$-canonical divisors. The incidence loci are defined by requiring divisors to have prescribed multiplicities at marked points. We compute classes closure in over curves with rational tails. expressed as a linear combination tautological indexed decorated stable graphs coefficients enumerating appropriate weightings. As consequence, we obtain an explicit expression for some relations rings