ag.algebraic geometry – admissible covers vs. stable maps to P^1

The paper Stable maps and tautological classes of Faber-Pandharipande shows that the Gromov-Witten classes on spaces of relative stable maps of the projective line push forward to tautological classes on moduli spaces of stable curves.

It is claimed on p. 6 that $overline{M}_{g,0}(mu_1,ldots,mu_m)=overline{H}_g(mu_1,ldots,mu_m)$, that is, the space of relative stable maps with ramification profiles $mu_i$ over marked points of $mathbb{P}^1$ is equal to the space of admissible covers of a genus 0 curve. However, I am confused as to how this can be correct: if the degree is 1, then I believe the space on the right is empty, but the space on the left has many components in general, coming from starting with the identity map on $mathbb{P}^1$ and attaching ghost components of positive genus to the source. More generally, I don’t see how the presence of ghost components allow one to identify a stable map with an admissible cover.

Later Proposition 1 it is stated as a corollary the fundamental class of $overline{H}_g$ pushes forward to a tautological class on $overline{M}_{g,n}$, but because of the discrepancy above I don’t see why this is immediate.

Am I missing something?

graph theory – Complexity of heaviest 2-optimal vertex-disjoint cycle covers

Calculating lightest vertex-disjoint cycle covers of finite complete symmetric graphs with weighted edges can be done efficiently and also renders the edge set of the calculated cycles free of pairs of crossing edges.

Calculating the unconstrained heaviest cycle cover will however generate edge sets with many pairs of crossing edges, leading to the

Question:
what is the complexity of calculating heaviest 2-optimal vertex-disjoint cycle covers, i.e. if constraints are added that make crossing edges mutually exclusive?

The motivation for the question is the observation that the minimal cycle cover may contain cycles that are far apart, thus making it hard to merge these cycle in an optimally to get an approximation of the shortest Hamilton cycle.
For heaviest 2-optimal cycle covers we may expect many pairs of long edges for which the minimum-weight matching of the $K_4$ that is induced by their adjacent vertices is small, thus easing the task of optimally merging the cycles to a short tour.

Galois covers of curves of arbitrary degree.

For smooth projective algebraic curves over finite fields. Do they admit a finite Galois cover of any degree, that is not induced by just base extension?

travel insurance covers between flight trip?

I have a travel insurance that would cover flight ie the departure (NYC) and the return (LA).

ie My departure date is DEC 15 and Return date is Jan 5

Trip details on the insurance document
Departure date  12/15/2020
Return date 01/05/2021
Trip deposit date   12/02/2020

If I make a round trip from LA Departure 12/23/2020 to Seattle Return LA 12/27/2020

Does a travel insurance cover between flight too ?

Many thanks!

These are an additional details –

Insured on Policy Trip

Coverages & Benefit Limits
Standard Packages
BAGGAGE COVERAGE
$750.00 Per Insured
BAGGAGE DELAY
$200.00 Per Insured
CONCIERGE SERVICES
Included    Per Insured
EMERGENCY EVACUATION AND REPATRIATION OF REMAINS
$150000.00  Per Insured
EMERGENCY TRAVEL ASSISTANCE
Included    Per Insured
NON-FLIGHT ACCIDENTAL DEATH & DISMEMBERMENT
$30000.00   Per Insured
PERSONAL SECURITY ASSISTANCE
Included    Per Insured
SINGLE OCCUPANCY
100% Trip Cost  Per Insured
TRAVEL MEDICAL ASSISTANCE
Included    Per Insured
TRAVEL MEDICAL EXPENSE
$15000.00   Per Insured
TRIP CANCELLATION
100% Trip Cost  Per Insured
TRIP DELAY
$500.00 Per Insured
$100.00 Payout Limit Per Day
TRIP INTERRUPTION
100% Trip Cost  Per Insured
TRIP INTERRUPTION-RETURN TRANSPORTATION ONLY
$500.00 Per Insured
WORLDWIDE TRAVEL ASSISTANCE
Included    Per Insured
15 Day Benefits
MISSED CONNECTION
$150.00 Per Insured
PRE-EXISTING CONDITION WAIVER
Included    Per Insured
TRIP CANCELLATION FOR DEFAULT
100% Trip Cost  Per Insured
TRIP INTERRUPTION FOR DEFAULT
100% Trip Cost  Per Insured

travel insurance covers between flight?

I have a travel insurance that would cover flight ie the departure (NYC) and the return (LA).

ie My departure date is DEC 15 and Return date is Jan 5

Trip details on the insurance document
Departure date  12/15/2020
Return date 01/05/2021
Trip deposit date   12/02/2020

If I make a round trip from LA Departure 12/23/2020 to Seattle Return LA 12/27/2020

Does the above insurance cover between flight too ?

Many thanks!

What are the scenes & monsters on the covers?

What are the scenes being portrayed on the covers of the Player’s Handbook (PHB), Dungeon Master’s Guide (DMG) and Monster Manual (MM) and what monsters do the scenes contain?

(Click for larger images.)
Player's Handbook Cover
Dungeon Master's Guide Cover
Monster Manual Cover

usability – Appropriate use of and child-proof alternatives to screwed-down battery covers

On lots of electronic devices with replaceable batteries, the battery cover is secured by a screw.

I understand that it may be necessary to protect against child access to the battery bay, but using a screw necessitates the use of a screwdriver to open the battery cover, which can be inconvenient. It annoys me to no end that I need to open my toolbox, grab my screwdriver, and unscrew the darn thing to replace the batteries.

When is using a screw appropriate for securing a battery cover? Under what circumstances is a simple latch closure inadequate for a battery cover? Are there safety regulations that cover this?


It appears that there are legal requirements that specify that toys intended for young children must have secured battery covers. However, this question covers more than just toys, but pretty much any electronic device that has replaceable batteries. Aside from safety and regulatory requirements, when is it better to use a screw instead of a latch closure to secure the battery cover?

Also, what alternatives are there to a screwed-down battery cover that can prevent young children from accessing batteries while being more convenient than a screw closure?

Any such battery compartment must be “inaccessible” such that “it is not physically exposed by reason of a sealed casing and does not become exposed through reasonably foreseeable use and abuse of the product” (source). This may be very difficult to attain in a toolless manner, but any ideas are welcome.

Smooth covers rescaling the symplectic form

Let $(M, omega)$ be a connected closed symplectic manifold of dimension $2n$.

Assume there exist smooth covering maps $phi_k:Mto M$ such that $phi_k^* omega=sqrt(n){k}omega$ for all $kgeq 1$. Is $n=1$ then?

dg.differential geometry – Covers of a 3-manifold pull back a cohomology class to any algebraic multiple

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at.algebraic topology – Smooth covers pulling back a cohomology class to any algebraic multiple

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