lefschetz theorem
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2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Hélène Esnault ◽  
Moritz Kerz

AbstractWe show that in positive characteristic special loci of deformation spaces of rank one $$\ell $$ ℓ -adic local systems are quasi-linear. From this we deduce the Hard Lefschetz theorem for rank one $$\ell $$ ℓ -adic local systems and a generic vanishing theorem.



Author(s):  
Luca Battistella ◽  
Navid Nabijou

Abstract We construct and study the theory of relative quasimaps in genus zero, in the spirit of Gathmann. When $X$ is a smooth toric variety and $Y$ is a smooth very ample hypersurface in $X$, we produce a virtual class on the moduli space of relative quasimaps to $(X,Y)$, which we use to define relative quasimap invariants. We obtain a recursion formula which expresses each relative invariant in terms of invariants of lower tangency, and apply this formula to derive a quantum Lefschetz theorem for quasimaps, expressing the restricted quasimap invariants of $Y$ in terms of those of $X$. Finally, we show that the relative $I$-function of Fan–Tseng–You coincides with a natural generating function for relative quasimap invariants, providing mirror-symmetric motivation for the theory.



Author(s):  
Helmut A. Hamm ◽  
Dũng Tráng Lê


Author(s):  
Ben Elias ◽  
Shotaro Makisumi ◽  
Ulrich Thiel ◽  
Geordie Williamson


2019 ◽  
Vol 347 ◽  
pp. 859-903
Author(s):  
Kalle Karu


2019 ◽  
Vol 52 (5) ◽  
pp. 1243-1264
Author(s):  
Tomoyuki ABE ◽  
Hélène ESNAULT
Keyword(s):  


2018 ◽  
Vol 371 (2) ◽  
pp. 755-776
Author(s):  
Beniamino Cappelletti-Montano ◽  
Antonio De Nicola ◽  
Juan Carlos Marrero ◽  
Ivan Yudin


2018 ◽  
Vol 222 (10) ◽  
pp. 3248-3254
Author(s):  
Charanya Ravi


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