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Tomas L. Gomez

Publications and source records attributed to Tomas L. Gomez.

At least 19 recordsLinked to original sources
arXiv2021

Automorphism group of the moduli space of parabolic bundles over a curve

We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking the dual, and Hecke transforms (using the filtrations given by the parabolic structure). A Torelli theorem for parabolic bundles with arbitrary rank and generic weights is also obtained. These results are extended to the classification of birational equivalences which are defined over "big" open subsets (3-birational maps, i.e. birational maps giving an isomorphism between open subsets with complement of codimension at least 3). Finally, an analysis of the stability chambers for the parabolic weights is performed in order to determine precisely when two moduli spaces of parabolic vector bundles with different parameters (curve, rank, determinant and weights) can be isomorphic.

math.AG↗
arXiv2021

On vector bundles over moduli spaces trivial on Hecke curves

Let $M_X(r,ξ)$ be the moduli space of stable vector bundles, on a smooth complex projective curve $X$, of rank $r$ and fixed determinant $ξ$ such that $°(ξ)$ is coprime to $r$. If $E$ is a vector bundle $M_X(r,ξ)$ whose restriction to every Hecke curve in $M_X(r,ξ)$ is trivial, we prove that $E$ is trivial.

math.AG↗
arXiv2019

Poisson structure on the moduli spaces of sheaves of pure dimension one on a surface

Let S be a smooth complex projective surface equipped with a Poisson structure s and also a polarization H. The moduli space M_H(S,P) of stable sheaves on S having a fixed Hilbert polynomial P of degree one has a natural Poisson structure given by s, studied by Tyurin and Bottacin. We prove that the symplectic leaves of M_H(S,P) are the fibers of the natural map from it to the symmetric power of the effective divisor on S given by the singular locus of s.

math.AG↗
arXiv2014

A GIT interpretration of the Harder-Narasimhan filtration

An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a "maximally destabilizing" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.

math.AG↗
arXiv2012

Automorphisms of moduli spaces of vector bundles over a curve

Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,Λ) be the moduli space of stable vector bundles over X or rank r and fixed determinant Λ, of degree d. We give a new proof of the fact that the automorphism group of M(r,Λ) is generated by automorphisms of the curve X, tensorization with suitable line bundles, and, if r divides 2d, also dualization of vector bundles.

math.AG↗
arXiv2011

Automorphisms of moduli spaces of symplectic bundle

Let X be an irreducible smooth complex projective curve of genus at least 3. Fix a line bundle L on X. Let M_{Sp}(L) be the moduli space of symplectic bundles (E, ExE ---> L) on X, with the symplectic form taking values in L. We show that the automorphism group of M_{Sp}(L) is generated by automorphisms sending E to ExM, where M is a 2-torsion line bundle, and automorphisms induced by automorphisms of X.

math.AG↗
arXiv2010

Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. II: The Second Year (2009-2010)

As an extension of the project in Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 61 SU UMa-type dwarf novae mainly observed during the 2009-2010 season. The newly obtained data confirmed the basic findings reported in Kato et al. (2009): the presence of stages A-C, as well as the predominance of positive period derivatives during stage B in systems with superhump periods shorter than 0.07 d. There was a systematic difference in period derivatives for systems with superhump periods longer than 0.075 d between this study and Kato et al. (2009). We suggest that this difference is possibly caused by the relative lack of frequently outbursting SU UMa-type dwarf novae in this period regime in the present study. We recorded a strong beat phenomenon during the 2009 superoutburst of IY UMa. The close correlation between the beat period and superhump period suggests that the changing angular velocity of the apsidal motion of the elliptical disk is responsible for the variation of superhump periods. We also described three new WZ Sge-type objects with established early superhumps and one with likely early superhumps. We also suggest that two systems, VX For and EL UMa, are WZ Sge-type dwarf novae with multiple rebrightenings. The O-C variation in OT J213806.6+261957 suggests that the frequent absence of rebrightenings in very short-Porb objects can be a result of sustained superoutburst plateau at the epoch when usual SU UMa-type dwarf novae return to quiescence preceding a rebrightening. We also present a formulation for a variety of Bayesian extension to traditional period analyses.

astro-ph.SR↗
arXiv2010

Einstein-Hermitian connection on twisted Higgs bundles

Let $X$ be a smooth projective variety over $\mathbb C$. We prove that a twisted Higgs vector bundle $(\calE\, ,θ)$ on $X$ admits an Einstein--Hermitian connection if and only if $(\calE\, ,θ)$ is polystable. A similar result for twisted vector bundles (no Higgs fields) was proved by S. Wang in \cite{Wa}. Our approach is simpler.

math.AG↗
arXiv2008

Torelli theorem for the Deligne--Hitchin moduli space

Fix integers $g\geq 3$ and $r\geq 2$, with $r\geq 3$ if $g=3$. Given a compact connected Riemann surface $X$ of genus $g$, let $\MDH(X)$ denote the corresponding $\text{SL}(r, {\mathbb C})$ Deligne--Hitchin moduli space. We prove that the complex analytic space $\MDH(X)$ determines (up to an isomorphism) the unordered pair $\{X, \overline{X}\}$, where $\overline{X}$ is the Riemann surface defined by the opposite almost complex structure on $X$.

math.AG↗
arXiv2008

Torelli theorem for the moduli space of framed bundles

Let X be an irreducible smooth complex projective curve of genus g>2, and let x be a fixed point. A framed bundle is a pair (E,ϕ), where E is a vector bundle over X, of rank r and degree d, and ϕ:E_x\to C^r is a non-zero homomorphism. There is a notion of (semi)stability for framed bundles depending on a parameter τ>0, which gives rise to the moduli space of τ-semistable framed bundles M^τ. We prove a Torelli theorem for M^τ, for τ>0 small enough, meaning, the isomorphism class of the one-pointed curve (X,x), and also the integer r, are uniquely determined by the isomorphism class of the variety M^τ.

math.AG↗
arXiv2006

Constraining the Kahler Moduli in the Heterotic Standard Model

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles, constrain the set of Kaehler moduli which give rise to realistic compactifications of the strongly coupled heterotic string. When vector bundles are constructed using extensions, we provide simple rules to determine lower and upper bounds to the region of the Kaehler moduli space where such compactifications can exist. We show how small these regions can be, working out in full detail the case of the recently proposed Heterotic Standard Model. More explicitely, we exhibit Kaehler classes in these regions for which the visible vector bundle is stable. On the other hand, there is no polarization for which the hidden bundle is stable.

hep-th↗
arXiv2003

Stable tensors and moduli space of orthogonal sheaves

Let X be a smooth projective variety over C. We find the natural notion of semistable orthogonal bundle and construct the moduli space, which we compactify by considering also orthogonal sheaves, i.e. pairs (E,ϕ), where E is a torsion free sheaf on X and ϕis a symmetric nondegenerate (in the open set where E is locally free) bilinear form on E. We also consider special orthogonal sheaves, by adding a trivialization ψof the determinant of E such that det(ϕ)=ψ^2 ; and symplectic sheaves, by considering a form which is skewsymmetric. More generally, we consider semistable tensors, i.e. multilinear forms on a torsion free sheaf, and construct their projective moduli space using GIT.

math.AG↗