ترغب بنشر مسار تعليمي؟ اضغط هنا

Simpson Filtration and Oper Stratum Conjecture

89   0   0.0 ( 0 )
 نشر من قبل Pengfei Huang
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we prove that for the oper stratification of the de Rham moduli space $M_{mathrm{dR}}(X,r)$, the closed oper stratum is the unique minimal stratum with dimension $r^2(g-1)+g+1$, and the open dense stratum consisting of irreducible flat bundles with stable underlying vector bundles is the unique maximal stratum.



قيم البحث

اقرأ أيضاً

For an abeloid variety $A$ over a complete algebraically closed field extension $K$ of $mathbb Q_p$, we construct a $p$-adic Corlette-Simpson correspondence, namely an equivalence between finite-dimensional continuous $K$-linear representations of th e Tate module and a certain subcategory of the Higgs bundles on $A$. To do so, our central object of study is the category of vector bundles for the $v$-topology on the diamond associated to $A$. We prove that any pro-finite-etale $v$-vector bundle can be built from pro-finite-etale $v$-line bundles and unipotent $v$-bundles. To describe the latter, we extend the theory of universal vector extensions to the $v$-topology and use this to generalize a result of Brion by relating unipotent $v$-bundles on abeloids to representations of vector groups.
67 - Jin Cao , Wenchuan Hu 2019
We show that the Friedlander-Mazur conjecture holds for a sequence of products of projective varieties such as the product of a smooth projective curve and a smooth projective surface, the product of two smooth projective surfaces, the product of arb itrary number of smooth projective curves. Moreover, we show that the Friedlander-Mazur conjecture is stable under a surjective map. As applications, we show that the Friedlander-Mazur conjecture holds for the Jacobian variety of smooth projective curves, uniruled threefolds and unirational varieties up to certain range.
235 - Clint McCrory 2009
Using the work of Guillen and Navarro Aznar we associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on Borel-Moore homology with Z/2 coefficie nts an analog of the weight filtration for complex algebraic varieties.
The classical additive Deligne-Simpson problem is the existence problem for Fuchsian connections with residues at the singular points in specified adjoint orbits. Crawley-Boevey found the solution in 2003 by reinterpreting the problem in terms of qui ver varieties. A more general version of this problem, solved by Hiroe, allows additional unramified irregular singularities. We apply the theory of fundamental and regular strata due to Bremer and Sage to formulate a version of the Deligne-Simpson problem in which certain ramified singularities are allowed. These allowed singular points are called toral singularities; they are singularities whose leading term with respect to a lattice chain filtration is regular semisimple. We solve this problem in the important special case of connections on $mathbb{G}_m$ with a maximally ramified singularity at $0$ and possibly an additional regular singular point at infinity. We also give a complete characterization of all such connections which are rigid, under the additional hypothesis of unipotent monodromy at infinity.
We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions, and derive applications regarding the local cohomological dimension, the Du Bois complex, loca l vanishing, and reflexive differentials associated to Z.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا