Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe $S_n$-equivariant top weight Euler characteristic of $M_{g,n}$
205
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We prove a formula, conjectured by Zagier, for the $S_n$-equivariant Euler characteristic of the top weight cohomology of $M_{g,n}$.
rate research
Read More
We continue our study on smooth complex projective varieties $X$ of maximal Albanese dimension and of general type satisfying $chi(X, omega_X)=0$. We formulate a conjectural characterization of such varieties and prove this conjecture when the Albanese variety has only three simple factors.
We show the $mathbb{A}^{1}$-Euler characteristic of a smooth, projective scheme over a characteristic $0$ field is represented by its Hochschild complex together with a canonical bilinear form, and give an exposition of the compactly supported $mathbb{A}^{1}$-Euler characteristic $chi^{c}_{mathbb{A}^{1}}: K_0(mathbf{Var}_{k}) to text{GW}(k)$ from the Grothendieck group of varieties to the Grothendieck--Witt group of bilinear forms. We also provide example computations.
Let $G$ be a simple complex algebraic group, $P$ a parabolic subgroup of $G$ and $N$ the unipotent radical of $P.$ The so-called equivariant compactification of $N$ by $G/P$ is given by an action of $N$ on $G/P$ with a dense open orbit isomorphic to $N$. In this article, we investigate how many such equivariant compactifications there exist. Our result says that there is a unique equivariant compactification of $N$ by $G/P$, up to isomorphism, except $P^n$.
We show a Z^2-filtered algebraic structure and a quantum to classical principle on the torus-equivariant quantum cohomology of a complete flag variety of general Lie type, generalizing earlier works of Leung and the second author. We also provide various applications on equivariant quantum Schubert calculus, including an equivariant quantum Pieri rule for any partial flag variety of Lie type A.
We study the topology of a space parametrizing stable tropical curves of genus g with volume 1, showing that its reduced rational homology is canonically identified with both the top weight cohomology of M_g and also with the genus g part of the homology of Kontsevichs graph complex. Using a theorem of Willwacher relating this graph complex to the Grothendieck-Teichmueller Lie algebra, we deduce that H^{4g-6}(M_g;Q) is nonzero for g=3, g=5, and g at least 7. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of another theorem of Willwacher, that homology of the graph complex vanishes in negative degrees.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
