Marc Anthony held out hope for a reconciliation with Jennifer Lopez, but decided to file for divorce when she told him ... she's madly in love with BF Casper Smart ... TMZ has learned.

TMZ broke the story ... Marc filed for divorce Monday -- nine months after the couple announced they were splitting.

But sources extremely close to Marc tell us, he didn't make the decision on his own -- he had a heart-to-heart with J.Lo a few weeks back to see if she really, truly wanted to end the marriage.

We're told he said he wanted to give the marriage another try, but Jennifer confessed ... she was deeply in love with Casper ... and wanted to pursue that relationship.

We're told Marc was blindsided ... he had not idea things were so serious -- and he was hurt.

So that's why Marc filed divorce papers this week.

Jennifer Lopez is drawing a line in the sand -- paying nearly a grand to rent out a public beach in L.A. last weekend ... to keep randoms away from her family and children.

Sources tell TMZ, Jennifer forked over $925 to the city of Long Beach to rent out Marine Beach on Saturday -- 3,400 feet of shoreline -- just for her, her kids, her BF Casper Smart and other family and friends.

To keep out the riffraff, we're told lifeguards marked off the water using buoys -- and kept the beach gates locked.

We're told J.Lo and co. brought their own jet skis for awesome fun times -- and even hired a wakeboard instructor.

Meanwhile, a bunch of sad locals stayed home and played with dirt.

Jennifer Lopez and her 24-year-old boyfriend Casper Smart were quite the lovebirds and enjoyed a Valentine's Day frolicking on the sand in Santa Barbara on Tuesday.

Besides holding hands and taking long walks on the beach, Jen even climbed up on top of Casper to ride the swing together.

In related news, Marc Anthony VD pics should surface in 5 ... 4... 3 ...

Jennifer Lopez showed off her 42-year-old mother of two taut flat stomach while in Malibu the other day.

The "American Idol" judge was looking belly good, as her 24-year-old boy toy lover Casper Smart frolicked on the sand with her daughter Emme.

Ticking off Marc Anthony is like a day at the beach.

Marc Anthony and Jennifer Lopez possibly getting back together means only one thing -- J.Lo's boy toy Casper Smart better enjoy the Bentley and those sweet vacas while he can! Tick, tock ...

Jennifer Lopez might want to think twice about handing Casper Smart the keys to her Bentley ... 'cause her BF just pleaded no contest in a drag racing case.

Casper's high speed bust came back in April 2010 -- long before his J.Lo days -- and today an LA County Superior Court judge hit him with 12 months probation and a $500 fine.

Casper wasn't required to be in court ... his attorney entered the plea. We're guessing speed racer had better people things to do.

With their Florida getaway still in full effect, Jennifer Lopez made sure to hold her boy toy Casper Smart's hand to safely maneuver down Miami's Lincoln Road this weekend.

The 24-year-old better know to look both ways before crossing ... J.Lo.

Boy toy extraordinaire Casper Smart is really cruising into Jennifer Lopez's life ... and rode around on a yacht with the pop icon and her two kids in Miami on Friday.

For J.Lo, 2012 is all about out with the old and in with the new ... arm candy. 

Banging Jennifer Lopez has some HUGE perks ... (besides just banging Jennifer Lopez) ... TMZ has learned her new boy toy is now driving around town in the pop star's pimped out BENTLEY!!!

Sources close to Casper Smart tell us ... the world's most famous backup dancer isn't just using the car to chauffeur his meal ticket around when she's in L.A. ... he gets the car for personal use too.

Besides car privileges ... dude has already flown across the world on a private jet ... gone on tropical vacations ... and as we previously mentioned, he gets to bang J.Lo.

Not bad for a 24-year-old, Mr. Smart.

Cris Judd ain't bitter that his ex-wife Jennifer Lopez found a younger, paler back-up dancer to mess around with ... dude tells TMZ he couldn't be happier for the pop star.

Judd married Lopez back in 2001 ... then divorced in 2002 ... and he's since re-married to a non-famous lady named Kelly A. Wolfe.

Don't hate -- appreciate.

She's not officially divorced, but Jennifer Lopez is living the single life -- hitting up a raging Hollywood nightclub last night with her new boy toy Casper Smart ... TMZ has learned.

The couple stopped by Boulevard 3 -- and sources tell us, J.Lo and Smart partied all night in a private area of the club ... dancing with each other and being very affectionate.

We ran into Smart on his way out -- but he was tight-lipped.